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# Solid angle

1. ### SpaceExplorer

25
What is a plane angle and a solid angle?(please provide diagram if possible) Also, what is the definition of 1 sr and 1 rad?

2. ### mathman

6,576
Sorry - no diagrams.

A plane angle is defined as the angle between two straight lines. To get the units, consider a circle of radius 1. The circumference is of length 2pi. The angle (radians) between two radii is defined by the length of the arc defined by the two radii.

A solid angle is defined in analogous way using a sphere of radius 1. The sphere has a surface area of 4pi. A solid angle (sphereradians) is defined by the area of a figure on the surface of the sphere. The solid angle is given as the angle from the center of the sphere, where the surface figure is traced back to the center. I know that this sounds clumsy, but think of it by starting with a spherical triangle, leading to a wedge shaped figure.

Note - this is a math question. It is not physics.

Last edited: Jun 2, 2008
3. ### tiny-tim

26,043
Welcome to PF!

Hi SpaceExplorer ! Welcome to PF!

I'll just add this to what mathman says:

Solid angle is like an area in your field of vision.

When a star moves across the sky, you measure that as an angle, of so many radians, as a fraction of 2π.

But you measure the "area" of the moon (or of the field of vision of a telscope) as a solid angle, of so many steradians, as a fraction of 4π.

4. ### Priya123

11
1 sr means 1 steradian steradian is the SI unit of solid angle and 1rad means 1 radian radian is the SI unit of plane angle. Plane angle is defined as:-
An angle of one radian results in an arc with a length equal to the radius of the circle.
Solid angle is defined as:-
the solid angle subtented at the centre of a sphere of radius r by a portion of the sphere whose area A,equals r square

5. ### Priya123

11
and this is physics not maths it is under the topic of measurements

6. ### Ken G

3,574
In case it isn't clear from the above, 1 steradian is the solid angle of 1/4pi fraction of the full field of view, the full sphere. So the physical area of an object at distance D that is curved in the shape of a piece of a spherical shell, and subtends 1 steradian of solid angle, is D2, and an object at that same distance that has a smaller than 1 steradian solid angle is proportionately smaller in area. (Usually we imagine it is not in the shape of a piece of a spherical shell, but it is also much much smaller than 1 steradian, so the area here is just the cross sectional area of the object.)

The radian works the same but in length-- an object that subtends 1 radian at distance D has length D along a piece of a circular arc. Again the formula becomes more useful for objects much smaller than 1 radian in angle, so the length is a kind of length perpendicular to the line of sight, rather than literally worrying about it being shaped like the arc of a circle.

7. ### Priya123

11
thats a more clearer way of my explanation and thanks it helped me out too

### Staff: Mentor

The original question was asked two and a half years ago, by the way.

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# Difference between revisions of "2001 AMC 8 Problems"

## Problem 1

Casey's shop class is making a golf trophy. He has to paint $300$ dimples on a golf ball. If it takes him $2$ seconds to paint one dimple, how many minutes will he need to do his job?

$\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12$

## Problem 2

I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 12$

## Problem 3

Granny Smith has $63. Elberta has$2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?

$\text{(A)}\ 17 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 23$

## Problem 4

The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 9$

## Problem 5

On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later, he heard the sound of thunder. The speed of sound is $1088$ feet per second and one mile is $5280$ feet. Estimated, to the nearest half-mile, how far Snoopy was from the flash of lightning?

$\text{(A)}\ 1 \qquad \text{(B)}\ 1\frac{1}{2} \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 2\frac{1}{2} \qquad \text{(E)}\ 3$

## Problem 6

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?

$\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140$

Problems 7, 8 and 9 are about these kites.

To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram below. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid. ￼$[asy] for (int a = 0; a < 7; ++a) { for (int b = 0; b < 8; ++b) { dot((a,b)); } } draw((3,0)--(0,5)--(3,7)--(6,5)--cycle); [/asy]$

### Problem 7

What is the number of square inches in the area of the small kite?

$\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 23 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 25$

### Problem 8

Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?

$\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 38 \qquad \text{(E)}\ 39$

### Problem 9

The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?

$\text{(A)}\ 63 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 189 \qquad \text{(E)}\ 264$

## Problem 10

A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?

$\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}$

## Problem 11

Points $A$, $B$, $C$ and $D$ have these coordinates: $A(3,2)$, $B(3,-2)$, $C(-3,-2)$ and $D(-3, 0)$. The area of quadrilateral $ABCD$ is

$[asy] for (int i = -4; i <= 4; ++i) { for (int j = -4; j <= 4; ++j) { dot((i,j)); } } draw((0,-4)--(0,4),linewidth(1)); draw((-4,0)--(4,0),linewidth(1)); for (int i = -4; i <= 4; ++i) { draw((i,-1/3)--(i,1/3),linewidth(0.5)); draw((-1/3,i)--(1/3,i),linewidth(0.5)); } [/asy]$

$\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 24$

## Problem 12

If $a\otimes b = \dfrac{a + b}{a - b}$, then $(6\otimes 4)\otimes 3 =$

$\text{(A)}\ 4 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 72$

## Problem 13

Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?

$\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 72$

## Problem 14

Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?

• Meat: beef, chicken, pork
• Vegetables: baked beans, corn, potatoes, tomatoes
• Dessert: brownies, chocolate cake, chocolate pudding, ice cream

$\text{(A)}\ 4 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 72 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 144$

## Problem 15

Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?

$\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 40$

## Problem 16

A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

$[asy] draw((0,8)--(0,0)--(4,0)--(4,8)--(0,8)--(3.5,8.5)--(3.5,8)); draw((2,-1)--(2,9),dashed); [/asy]$

$\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{2} \qquad \text{(C)}\ \dfrac{3}{4} \qquad \text{(D)}\ \dfrac{4}{5} \qquad \text{(E)}\ \dfrac{5}{6}$

## Problem 17

For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the following table (where K = 1000).

$$\begin{tabular}{rccccccccccccccc} \text{Question} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \text{Value} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K} \end{tabular}$$

Between which two questions is the percent increase of the value the smallest?

$\text{(A)}\ \text{From 1 to 2} \qquad \text{(B)}\ \text{From 2 to 3} \qquad \text{(C)}\ \text{From 3 to 4} \qquad \text{(D)}\ \text{From 11 to 12} \qquad \text{(E)}\ \text{From 14 to 15}$

## Problem 18

Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?

$\text{(A)}\ \dfrac{1}{36} \qquad \text{(B)}\ \dfrac{1}{18} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{11}{36} \qquad \text{(E)}\ \dfrac{1}{3}$

## Problem 19

Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?

$[asy] unitsize(12); draw((0,9)--(0,0)--(9,0)); label("time",(4.5,0),S); label("s",(0,7),W); label("p",(0,6),W); label("e",(0,5),W); label("e",(0,4),W); label("d",(0,3),W); label("(A)",(-1,9),NW); draw((0,4)--(4,4),dashed); label("M",(4,4),E); draw((0,8)--(4,8),linewidth(1)); label("N",(4,8),E); draw((15,9)--(15,0)--(24,0)); label("time",(19.5,0),S); label("s",(15,7),W); label("p",(15,6),W); label("e",(15,5),W); label("e",(15,4),W); label("d",(15,3),W); label("(B)",(14,9),NW); draw((15,4)--(19,4),dashed); label("M",(19,4),E); draw((15,8)--(23,8),linewidth(1)); label("N",(23,8),E); draw((30,9)--(30,0)--(39,0)); label("time",(34.5,0),S); label("s",(30,7),W); label("p",(30,6),W); label("e",(30,5),W); label("e",(30,4),W); label("d",(30,3),W); label("(C)",(29,9),NW); draw((30,4)--(34,4),dashed); label("M",(34,4),E); draw((30,2)--(34,2),linewidth(1)); label("N",(34,2),E); draw((0,-6)--(0,-15)--(9,-15)); label("time",(4.5,-15),S); label("s",(0,-8),W); label("p",(0,-9),W); label("e",(0,-10),W); label("e",(0,-11),W); label("d",(0,-12),W); label("(D)",(-1,-6),NW); draw((0,-11)--(4,-11),dashed); label("M",(4,-11),E); draw((0,-7)--(2,-7),linewidth(1)); label("N",(2,-7),E); draw((15,-6)--(15,-15)--(24,-15)); label("time",(19.5,-15),S); label("s",(15,-8),W); label("p",(15,-9),W); label("e",(15,-10),W); label("e",(15,-11),W); label("d",(15,-12),W); label("(E)",(14,-6),NW); draw((15,-11)--(19,-11),dashed); label("M",(19,-11),E); draw((15,-13)--(23,-13),linewidth(1)); label("N",(23,-13),E); [/asy]$

## Problem 20

Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).

$\text{(A)}\ \text{S,Q,M} \qquad \text{(B)}\ \text{Q,M,S} \qquad \text{(C)}\ \text{Q,S,M} \qquad \text{(D)}\ \text{M,S,Q} \qquad \text{(E)}\ \text{S,M,Q}$

## Problem 21

The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is

$\text{(A)}\ 19 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 40$

## Problem 22

On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?

$\text{(A)}\ 90 \qquad \text{(B)}\ 91 \qquad \text{(C)}\ 92 \qquad \text{(D)}\ 95 \qquad \text{(E)}\ 97$

## Problem 23

Points $R$, $S$ and $T$ are vertices of an equilateral triangle, and points $X$, $Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?

$[asy] pair SS,R,T,X,Y,Z; SS = (2,2*sqrt(3)); R = (0,0); T = (4,0); X = (2,0); Y = (1,sqrt(3)); Z = (3,sqrt(3)); dot(SS); dot(R); dot(T); dot(X); dot(Y); dot(Z); label("S",SS,N); label("R",R,SW); label("T",T,SE); label("X",X,S); label("Y",Y,NW); label("Z",Z,NE); [/asy]$

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 20$

## Problem 24

Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?

$[asy] draw((0,0)--(4,4*sqrt(3))); draw((1,-sqrt(3))--(5,3*sqrt(3))); draw((2,-2*sqrt(3))--(6,2*sqrt(3))); draw((3,-3*sqrt(3))--(7,sqrt(3))); draw((4,-4*sqrt(3))--(8,0)); draw((8,0)--(4,4*sqrt(3))); draw((7,-sqrt(3))--(3,3*sqrt(3))); draw((6,-2*sqrt(3))--(2,2*sqrt(3))); draw((5,-3*sqrt(3))--(1,sqrt(3))); draw((4,-4*sqrt(3))--(0,0)); draw((3,3*sqrt(3))--(5,3*sqrt(3))); draw((2,2*sqrt(3))--(6,2*sqrt(3))); draw((1,sqrt(3))--(7,sqrt(3))); draw((-1,0)--(9,0)); draw((1,-sqrt(3))--(7,-sqrt(3))); draw((2,-2*sqrt(3))--(6,-2*sqrt(3))); draw((3,-3*sqrt(3))--(5,-3*sqrt(3))); [/asy]$

$\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9$

## Problem 25

There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?

$\text{(A)}\ 5724 \qquad \text{(B)}\ 7245 \qquad \text{(C)}\ 7254 \qquad \text{(D)}\ 7425 \qquad \text{(E)}\ 7542$

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Converging Product

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Binary Squares

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

Golden Fibs

Stage: 5 Challenge Level:

The Fibonacci recurrence relation gives a relationship between the first three terms of the sequence and, if it is also a geometric sequence with common ratio $r$, then this relation gives a quadratic equation in $r$. The question asks for both the result and also its converse to be proved.


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# The Debt Ceiling: This is getting ridiculous

Discussion in 'Politics' started by Xelor, Sep 7, 2017.

1. ### XelorRegistered Member

Messages:
82
Just how lame are the people whom Americans have elected to Congress? Rather than voting to discard the debt ceiling or to appropriate most but not all of the money available for a given fiscal year, the Congress have stood by the notion of having a debt ceiling and periodically increasing it. Come on! What substantive value is there to having a debt ceiling when all that happens is they keep increasing it?

FEMA's Disaster Relief Fund (DRF) is set to be exhausted this coming Friday. Why? Well, largely because Harvey was a more devastating disaster than the government wagered would hit the U.S. Absent Harvey, or with a less impactful Harvey, the DRF would quite likely not have run out of money and necessitated the GOP-held Congress [1] propose and pass a debt ceiling increase (along with in turn borrowing more money), in order to not only provide assistance to disaster victims but also to avoid appearing as penurious "fat cats."

Would it have been so bad for Congress to have appropriated what they could, and held back, say, $100B or so from the total$1T+ available for discretionary spending?

Quite simply, for a given time period and set of objectives, if one has a fixed sum of money available for budgeting, it's absurd to allocate and spend every last dollar of that sum to fund one's routine endeavors, thereby, in the event of an unforeseen, and unforeseeable at the time of appropriating the budget, disaster (natural or manmade), having only the options of increasing the debt ceiling or leaving citizens "high and dry," so to speak. I mean, seriously, who having a total budget of billions and billions of dollars does that? Um....The members of the U.S. Congress do that.

Then there is the matter that this time round, it's hurricane Harvey relief that, in part, necessitates the increase. Even the most ardent AGW-deniers assert not that the planet isn't warming, but rather that it is not warming because of human activity. Accordingly, regardless of warmer seas' etiology, the fact remains that a consequence of them is more powerful hurricanes. [2] Does not the better part of prudence oblige Congress, one having a debt ceiling, to appropriate funds such that it doesn't have to raise it when reasonably foreseeable calamities like weather events happen mere weeks before the federal fiscal year ends? After all, it's not as though hurricane and tornado events -- unlike, earthquakes, and/or volcanic eruptions -- don't come almost every year.

On the contrary, they occur with such regularity that we have identified seasons for them [3], and they consistently wreak more widely spread devastation and directly disrupt the lives of more U.S. citizens than any band of terrorists. Does Congress adopt a "let's hope it doesn't happen" stance when funding DHS and the USIC agencies? Seemingly not; they aren't the organizations that have run out of money and nobody's saying the debt ceiling increase is to provide funding for them.

At the end of the day, however, the debt ceiling serves as little more than politically induced stress. That's stress that workers and beneficiaries just don't need in their lives.

Note(s):
1. Congress, not the POTUS, has the power of the purse and Congress designates how much money gets assigned to each government program. I mention the GOP only because it is the GOP that's most ardent about debt and deficit reduction and about reducing government spending. One'd think, therefore, that the GOP would only pass budgets that don't put the government in the position of needing to pass stopgap debt ceiling increases.

• History, rationale, politics and management of the national debt and the debt ceiling:

douwd20 likes this.

3. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
It is has long been ridiculous. It baffles the mind every time I hear a right-wing politician explain how we can default without really defaulting. But their base, i.e. Republicans, eat that shit up and that's why the do it. The debt ceiling is easy bait for demagogues. That's why Congress continues to do what it has always done. If say Democrats were to try to do away with the debt ceiling, Republicans would demagogue the issue to hell and back. That's why neither party will eliminate the debt ceiling. Most Americans don't understand it, and that makes it easy picking for the demagogues.

5. ### iceauraValued Senior Member

Messages:
25,619
The Republican Congress has been acting like this since 1992. That's 25 years, if anyone's keeping score.

7. ### mathmanValued Senior Member

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1,473
Today's news? Trump and Congressional Democrats reach agreement to permanently remove the debt ceiling.

8. ### iceauraValued Senior Member

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25,619
Trump backed Schumer's proposal of a short term (three month) debt ceiling hike.

It still has to pass Congress - Trump has no vote, and the Dems are minority. But it's likely now.

There is no agreement to remove the debt ceiling permanently - Trump has mentioned it, and may or may not favor it when action time comes, but that's not the current deal. Three months from now we do it all over again.

9. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
Your point combining future weather catastrophe and money needed to secure and rebuild etc. is really valid IMO and one that needs to be discussed.
I and others, have often stated that it is only when the insurance industry ( or any post catastrophe financial support structures) start to fail that Climate change and the consequences of such will actually be taken seriously.

That time is upon us now, or it will be very shortly.

It is a no brainer to state with almost 100% certainty, that if the ocean waters are warming up the evaporation rates are increasing. This leads to an incredible and extremely rapid increase in the amount of mass floating around in our atmosphere. Obviously this MUST with out any doubt lead to a massive increase in the extreme nature of storms, hurricanes and cyclones etc. in the short to medium term future. Where it actually leads to in the longer term is another even more challenging question/answer but... the point is that there IS NO DOUBT that extreme weather events such as Hurricane Harvey, Irma etc are not only going to become more and more frequent but also more and more extreme and very quickly...

Now that being said the ability to recover from these storms is and will become more and more problematic, difficult, if not impossible, as the money to do so runs out. So it is really important to realize that if it isn't this year it may be next or the one after that we are simply going to have to abandon regions due to the incapacity to restore them.

"Building infrastructure to withstand winds in excess of 300kph and huge rainfall inundations is incredibly expensive"
but that is what we have to seriously start thinking about doing...

Last edited: Sep 8, 2017
10. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
Well, here is the thing, in the US we have a federal flood insurance program to cover incidents like this. So while insurance companies will pay a portion of these costs the federal government will pay the lions share of these costs. US insurance companies will come out of this smelling like roses. They will raise rates next year and will soon be flushed with cash. I'll be buying insurance stocks in a few days. We've been through this many times before and it's always the same.

Last edited: Sep 8, 2017
11. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
Things change... and one wonders where the money is going to come from not only for this year Harvey and Irma and possibly others but subsequent years , year after year of worsening conditions.

12. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
It will come from the US taxpayer. Congress approved 15 billion dollars for Texas today. https://www.nytimes.com/2017/09/07/us/politics/senate-harvey-irma-aid.html

13. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
do you believe the situation for the short to medium term future is tenable? ( funding disaster relief for the next say 10 years)

14. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
The sheer cost of having a city like Houston off line for a week or more must be staggering...

15. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
They haven't been much of a problem in the past. But I expect with global warming they will become more and more frequent and more damaging. Eventually, something will be done. I'm not sure what. But something will be done. New Orleans is on the coast and below sea level. That's a problem. Houston is just a few feet above seal level. We have built cities in very low lying areas that are very prone to flooding. The best solution is to recognize global warming and work to mitigate it.

16. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
In the overall scope of things it's not that much. There will be a short downturn. But federal money and insurance money will flood back into the area, and it will be an economic boon. Houses, roads, and other infrastructure will need to be rebuilt. It will actually be a boon to the economy. In Texas most of the oil infrastructure is up and running. Most of the refiners are back on line. Refiners are making a mint because gasoline prices are up 20% or more.

Last edited: Sep 8, 2017
17. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
You are really missing my point...
It may very well be a boon for local economy...but someone is paying for it...

Have they finished paying for Katrina yet? Do you know?

How many times a year and for how many years can you borrow and spend "20 billion dollars" on disaster relief? ( plus pay interest)

Last edited: Sep 8, 2017
18. ### joepistoleDeacon BluesValued Senior Member

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22,880
It depends on what you mean by "pay for". Yeah, the Katrina bills have been paid. These disasters are boons for the local economies and for the larger economy as well. Insurance companies are paying for it, but the federal government is paying for the lions share of it. Some people will be hurt, e.g. the people who don't have insurance. Some people will lose their businesses. Some companies will lose business, e.g. cruise lines. But they will aren't going away.

19. ### XelorRegistered Member

Messages:
82
That's plausible; however, I don't know that even if it's taken seriously, it'll be understood by most voters. How insurance companies function and the structure of the insurance industry isn't well understood by many and even fewer understand actuarial risk. There's also the matter that insurance companies hold about 11% to 15% of commonly traded equities, which means if they find themselves in dire straits, they'll sell them, thus triggering a huge drop in the stock market. That could very easily lead not to Great Recession II, but Great Depression II.

I suppose we'll have to wait and see, but the "triple punch" of Harvey, Irma and Jose (?) could alone do it. (Only the "flood exclusion" may be all that keeps insurance industry collapse at bay.) The three combined with some other calamity -- KJU's foolishness, a big quake on the West Coast or a WTC-scale terrorist strike -- almost certainly would, IMO, trigger a Great Recession II, one made even worse by the antics of our loose-cannon "Tweeter in Chief."

20. ### joepistoleDeacon BluesValued Senior Member

Messages:
22,880
Here is the thing, the US government can spend as much money as necessary. It has unlimited ability to spend money. Unlike you and me, the federal government can print as much money as it needs. It can handle any thing short of a cataclysmic species ending event providing it acts appropriately. With Republicans in control of Washington, that may not always be the case. I'm no supporter of Trump, but he does have people around him who know the score, and given his concern with raising the debt ceiling, I think he gets it. Congressional Republicans on the other hand probably don't.

21. ### Quantum QuackLife's a tease...Valued Senior Member

Messages:
17,914
From a layman's perspective there is only one thing one needs to keep in mind.
Insurance companies are there to make a profit and like all companies when they do not believe they can turn a profit on a product they stop offering that product.
Now if I am not mistaken, and I probably are, most financial lending, borrowings, mortgages etc requires insurance against such disasters like fire flood and tempest, loss of income etc. and if these products are not available or are way too expensive to purchase then what happens to the finance industry, the end consumer and so on.. etc....

22. ### XelorRegistered Member

Messages:
82
Be that as it may, the lost productivity, revenue and innovation is, for all intents and purposes, forever lost. When a business or economy loses resources, even if the resources' impotence is short-lived, very few of them recover and outstrip their prior performance to the extent that the loss is made up for. Quite simply, very few organizations, economies and individuals rebound on the scale that, say, Apple did.

23. ### XelorRegistered Member

Messages:
82
Yes, the ripple effect to which you and I have alluded is very real, and very hard to stop once it's underway.


text:
This collection of area worksheets encompasses a variety of PDFs to find the area of trapezoids whose dimensions are given as integers, fractions and decimals. Just Scroll Down To View and Print. Approx. To be used after both area and Circumference has been taught as a consolidation lesson or as a revision lesson towards exam time. Equip future architects, aeronauts, coast guards, graphic designers with this meticulously designed assemblage of printable area worksheets to figure out the area of irregular figures, area of 2D shapes like squares, rectangles, triangles, parallelograms, trapezoids, quadrilaterals, rhombus, circles, polygons, kites, mixed and compound shapes using … Applying the formula, Circumference = 2 * pi * r, find the circumference of each circle. Worksheets to Supplement our Lessons. hours? The exercises are presented as geometric illustrations and also in word format. Area And Perimeter Worksheets With Answers Pdf high resolution. Previous Types of Triangle Textbook Answers … We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step! our costs. Do you know how old you are...in weeks? This page has links to worksheets on areas of rectangles, triangles, trapezoids, circles, and more. Find the area of triangles, worksheet #2. These worksheets are prepared for class practice / additional practice assignments / practice from home. area and Perimeter Word Problem Worksheets … Find the diagonal lengths, missing parameters, compute the area, learn to convert to a specified unit and much more. My students really enjoy these worksheets because each page includes a fun activity. Always appreciate your a triangle can also visit the definitions of regular polygons. Name: Super Teacher Worksheets - www.superteacherworksheets.com Area of a Rectangle Find the area of each rectangle. We offer a wide range of printables for this area (no pun intended). Copyright © 2021 - Math Worksheets 4 Kids, Parallel, Perpendicular and Intersecting Lines. Areas of Rectangles and Squares. These worksheets are perfect for homework, classwork, and centers. Measure the length and the width with a ruler in inches or centimeter to find the area of a rectangle Area of rectangles worksheet 4. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Worksheet by Kuta Software LLC Geometry HW 70 Area: Rectangles, Triangles, Parallelograms, Trapezoids ... [0D1J6o fKvuvtcaK SioEfctWwqaDrGeS gLZL_Ct.w k aAulQlc arDiwg[hwt\sJ erXeEswemrkvoeydL.-1-Find the area of each. Confirm your consent, regular polygons worksheet answers is experiencing technical difficulties. Area And Perimeter Word Problems Worksheets Pdf With Answers pics and pictures collection that … Area: Counting Square Units (Very Basic) Find the area of the shapes by counting the number of square unit tiles shown. Worksheet(s) or assignment. Area of Circles Worksheet 5 – Here is a nine problem worksheet that will allow your students to practice calculating the area of a circle. Answer. \$6.97. Printable Math Worksheets @ www.mathworksheets4kids.com Name : Score : Measure the length of each bar. Give learning a head start with these finding the area of a square worksheets. The area of a parallelogram worksheets comprise adequate skills to find the area of a parallelogram, compute the value of the missing dimensions - base or height, practice finding the area by converting to specific units and more. All Rights Reserved. ID: 438384 Language: English School subject: Math Grade/level: Grade 6 Age: 7-11 Main content: Area Other contents: Compound Shapes Add to my workbooks (35) Download file pdf Embed in my website or blog Add to Google Classroom Learn to find the area or circumference using the given radius or diameter, calculate the area and circumference, compute the radius and diameter from the area or circumference given and a lot more. Info. By Amanda (Post) Pertl @ Math. Everything from area and circumference, radius, angles and tangents are provided for all abilities to whizz through. If the shape is measured in cm, then the area would be measured in square cm or cm. Simple plane shapes like triangles, rectangles, squares, parallelograms, rhombus, trapezoids, circles, semicircles, and quadrants compose the figures in our pdf area of composite shapes worksheets. Here you'll find a series of worksheets on area of trapezoids and parallelograms. plot and write coordinates in the first quadrant. Pinpoint-Learning-Area-and-Perimeter-Problems-Solutions. 1 cm 1 cm 1 cm 1 cm = 1 cm2 a. Apr 21, 2020 - √ area and Perimeter Word Problems Worksheets Pdf with Answers . Why not try one of our free printable math games with your students! 21) area = 201.1 in² 22) area = 78.5 ft² Find the circumference of each circle. please consider making a small donation to help us with Calculate the area of quadrilaterals whose dimensions are presented as whole numbers and fractions. The area of a 2D shape is the amount of space it takes up in 2 dimensions, and its units are always squared, e.g \text{cm}^2,\hspace{1mm}\text{m}^2. Our perimeter and area worksheets are designed to supplement our Perimeter and Area lessons. When you are done, just click "Back" on your browser. Area of a Circle Textbook Answers answers; Post navigation. Determine the missing parameters by substituting the values in the formulas, solve exercises involving unit conversions too. 23 area and Perimeter Word Problems Worksheets Pdf with Answers . Find the areas of the rectangles and squares by using the formula area = length times width. DIGITAL PDF AND PRINTABLES: These printable area and perimeter worksheets work well for 4th grade test prep, as a math center review, as homework, for morning work or as a formative assessment or quiz. with each donation! Free printable circumference, radius, diameter and area of a circle worksheets with answer keys. The focus is on calculating the area of triangles and different quadrilaterals. Pin 28 Facebook Tweet. Report a problem. Videos and Worksheets; Primary; 5-a-day. These sheets are designed for kids from 3rd to 5th grade. The sheets are all graded in order from easiest to hardest. Resource type. pdf, 713 KB. You need to know the formulas to calculate the areas of some common shapes and be able to rearrange them. Free PDF download of Standard 10 Surface Area and Volume Worksheets with answers will help in scoring more marks in your class tests and school examinations, click links below for worksheets with important questions for Class 10 Surface Area and Volume chapter wise with solutions Basic instructions for the worksheets. We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page. Area and Perimeter Worksheets. About this resource. Include UNITS in your answers. Videos and Worksheets; Primary; 5-a-day. By Amanda (Post) Pertl @ Math. Many thanks to Lois Lewington for correcting a few repeats and providing the solutions to the questions for us. Find a variety of free printable worksheets for practicing both perimeter and area. Free PDF download of Standard 7 Perimeter and Area Worksheets with answers will help in scoring more marks in your class tests and school examinations, click links below for worksheets with important questions for Class 7 Perimeter and Area chapter wise with solutions ... Fine the perimeter and circumference of common shapes, worksheet #2. Each problem needs to be identified as either an area problem or a perimeter problem and then solved.. Augment your practice on finding the area with our area of rectilinear figures worksheets! Read Online Area And Perimeter Worksheet Answers Area And Perimeter Worksheet Answers Getting the books area and perimeter worksheet answers now is not type of inspiring means. These worksheets are from preschool, kindergarten to sixth grade levels of maths. After students have learned how to find the area of different shapes then they can practice these mixed problems of finding areas. Menu Skip to content. Area and Perimeter Worksheets & Printables. Level 2. Using these sheets will help your child to: know how to calculate the area of a triangle; know how to calculate the area of a range of quadrilaterals. Area of Trapezoids | Decimals – Type 1. You're going to find a many basic printable worksheets and … To find the circumference, multiply diameter with pi value. Explore & experience more than 1000 worksheets used under the topic of geometry & shapes in common core math lessons for grade-1, … The children of grade 5, grade 6 and grade 7 can reinforce their skills in finding the area of mixed shapes by practicing this set of printable worksheets. Before you sign up for the survey, make sure that you have read the guidelines and instructions. Drum into the heads of students the formula for the area of trapezoids A = (b 1 + b 2) h/2, where b 1 and b 2 are the base lengths and h is the height as they do this set of pdf area of a trapezoid worksheets. Surface Area . The problems on the sheet are identical, but the measurements get progressively harder to do! know how to find the area (and perimeter) of a rectangle; know how to find the area (and perimeter) of rectilinear shapes; Area is the amount of space that is inside a shape. days? These sheets involve reading scales going up in halves, ones, fives, tens, fifties and hundreds to find the length, weight or liquid capacity. This page has geometry activities related to circles. ... PDF with answer key: Created: Nov 27, 2017. Help your middle and upper primary school (Years 3, 4, 5, and 6) students work on their ability to calculate the area of different regular shapes with these differentiated area of different shapes worksheets in PDF format. Area and Perimeter Worksheets & Printables. Students should express their answers in the correct units of measurement. (a) … Geometry & Shapes Worksheets with Answers - Print & Download. Worksheet 1 : Worksheet 1 Key: Worksheet … We obtain this awesome picture from internet and choose the top for you. Get a free sample copy of our Math Salamanders Dice Games book By the time your class has completed this extensive series, they will undoubtedly be experts at finding the area of a circle. All the sheets in … © 2010-2021 Math Salamanders Limited. Recommended for grade 3, grade 4, grade 5 and up. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; September 20, 2018 August 22, 2019 corbettmaths. Each exercise provides a drawing of the circle as well as the length of either the radius or the diameter. Included here area exercises to count the squares in the irregular figures and rectangular shapes. Then draw a square with an area that is 9 times greater. Areas of Rectangles and Squares. Count the square units to find the area of a triangle. answers; Post navigation. Develop practice in finding the area of a segment of a circle with these practice pdfs. These are the figures that contain 2 or more shapes. Area … Our surface area worksheets are designed for students between 5th grade and 8th grade. Using given measurements, students find perimeter … Purc. Worksheets with answers are an effective method of helping young children learn their numbers, percentages, shapes, fractions, ratios – you name it, they’ll learn it through our maths practice worksheets. Learn to solve operations in order: parenthesis, exponents, multiply & divide, add & subtract. Search . pdf, 713 KB. Need help with printing or saving? Various shapes and units of measurement are used. There are three formative assessments for this standard each with ten questions. We have some great games for you to play in our Math Games e-books! 5 page PDF. Equip future architects, aeronauts, coast guards, graphic designers with this meticulously designed assemblage of printable area worksheets to figure out the area of irregular figures, area of 2D shapes like squares, rectangles, triangles, parallelograms, trapezoids, quadrilaterals, rhombus, circles, polygons, kites, mixed and compound shapes using appropriate area formulas. All children learn differently and work at their own levels and pace but we have resources for kids of all learning preferences. Reaffirm the concept of finding the area of a circle by using these practice worksheets. This set of middle school pdf worksheets comprises problems offered in three different formats, whose measures are given as integers. Find the area of triangles and parallelograms, worksheet #1. The area of a rectangular sheet is 500 cm2. Diameter and Circumference of a Circle worksheet Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Worksheet 5 If you are measuring the area of a rectangle, then the area will equal the length multiplied by the width. Some have missing information that the students will need to figure out before they can proceed with an answer. We have fun and challenging surface area and volume pdf worksheets on a range of topics, including calculating the area of rectangular prisms and the volume and surface area of cones and spheres. Worksheet 1 : Worksheet 1 Key: This section contains worksheets on area at a 5th and 6th grade level. Answer. Welcome; Videos and Worksheets; Primary; 5-a-day. Learn to find area of different shapes like circle, square, rectange, parallelogram and triangle with math area worksheets for kids. All you need to do is print. Incorporate these area of polygons worksheets comprising examples and adequate exercises to find the area of regular polygons like triangles, quadrilaterals and irregular polygons using the given side lengths, circumradius and apothem. Find the area of squares, rectangles, triangles, and circles. which will help your child to learn to work out the areas of a range of rectangles and rectilinear shapes. On the next grid, draw a square that has an area of 4 units. Includes basic, intermediate, and advanced-level worksheets. Area of Circles Worksheet 1 – Here is a nine problem worksheet that will allow your students to practice calculating the area of a circle. Videos, worksheets, 5-a-day and much more. learn the formulas to calculate the area of triangles and some quadrilaterals. Using these sheets will help your child to: work out the areas of a range of rectangles; find the area of rectilinear shapes. Word Doc PDF Find the area of triangles, parallelograms, trapezoids, and circles. This section contains worksheets on area at a 5th and 6th grade level. 23) area = 64 π mi² 24) area = 16 π in² Find the area of each. Multiply the base and height and divide by two, to calculate the area. The area of the rectangle below is 5 x 3 = 15 squares. PDF (15.34 MB) This is a collection of 55 Fun and Educational Area & Perimeter Worksheets! With area of a rectangle worksheets, your child will learn how to calculate area and use algebra to find the missing length of a rectangle. Calculate the area of rectangles, squares, triangles, parallelograms, trapezoids, and circles. Area of Rectilinear Shapes 1 (easy - 3rd Grade), Area and Perimeter Word Problems Sheet 1A, Area and Perimeter Word Problems Sheet 1B, Area and Perimeter Word Problems Sheet 1C, Converting Decimals to Fractions Worksheets, Multiplying Negative Numbers Online Practice, Subtracting Negative Numbers Online Practice. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. find the volume of shapes by counting cubes. Students find the areas of the individual rectangles and add them together. Strengthen skills in finding the area of a rectangle with these pdf worksheets featuring topics such as determine the area of rectangles, area of rectilinear shapes, rectangular paths and solve word problems. 33 Area and Perimeter F G to E 33 34 Volume of cuboids F G to E 34 35 Converting Metric Measures F G to E 35 36 Triangles, Quadrilaterals & Other Polygons F G to E 36 37 Names of solids F G to E 37 38 Tessellations F G to E 38 39 Isometric drawing F G to E 39 40 The probability scale F G to E 40 41 The averages F G to E 41 42 Pictograms F G to E 42 Find the area of parallelograms. Printable PDF KS3 and KS4 Circles Worksheets with Answers Learning the ins and outs of circles is an important part of maths for your child or student. Find the area of squares, rectangles, triangles, and circles. All the sheets in … Free worksheets are also included. You're going to find a many basic printable worksheets and … A = P = c. A = P = d. A = P = e. A = P = f. A = P = g. A = P = h. A = P = i. [2] 2. Search form. Area of triangles worksheet 5. Improve efficiency in finding the area of kites with these printable worksheets comprising illustrations and exercises in word format. This is just one of a set of 10 worksheets. Looking for a fun and motivating way to learn and practice math skills? Categories & Ages. Round the answer to 2 decimal places in these worksheets, recommended for middle school children. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Functional Maths - measures, shape & space. Maths. Each worksheet is randomly generated and thus unique. grade levels: 5th grade, 6th grade and 7th grade. Updated: Feb 22, 2018. pdf, 722 KB. Videos and Worksheets; Primary; 5-a-day. Worksheets to Supplement our Lessons . This worksheet will challenge your third graders with problems on area, perimeter, measurement, and elapsed time problems. To get the PDF worksheet, simply … The sheets are all graded in order from easiest to hardest. If you are a regular user of our site and appreciate what we do, Area of circle Math Worksheet for kids with answer key. Calculate the area of the kite, find the missing diagonal lengths using the area and much more! Our surface area worksheets are designed for students between 5th grade and 8th grade. Figure out the area of squares using the formula, determine the side lengths, find the length of the diagonals and calculate the perimeter using the area as well. It is possible that you could purchase the wrong domain name and not get the results that you need. Area and Perimeter (Debbie Jackson); Area and Perimeter Investigation (Catherine Roe) DOC; Perimeter Resources (3 Sheets) (Zainab Syed) DOC Symmetry (Sarah Pascall) ; Unit 8: Measure Problems and Coordinates (Dot Hullah); Finding the Perimeter (Tony Chapman); Finding Area (Tim Oran); Perimeter (Tim Oran); Area of Rectangles (2 sheets) (Michele Zylstra) PDF Area of Shapes (Decie Roberts) DOC PDF (3.72 MB) This unit includes area activities, worksheets, games, mini-lessons, and interactive notebook pages to help students practice finding missing sides when given the area or perimeter or when students are comparing area and perimeter. Feb 11, 2020 - Area And Perimeter Word Problems Worksheets Pdf With Answers – This awesome picture selections about Area And Perimeter Word Problems Worksheets Pdf With Answers is available to save. A common difficulty faced by students is how to convert between units of area and volume. The second section features shapes that must be measured by the student first. Suitable for KS3 and KS4. Area of a Trapezium Textbook Answers trapezia, trapeziums. Round your answer to the nearest tenth. Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance Be sure to also check out the fun perimeter interactive activities below! Perimeter and Area of Polygons Worksheets. Using these sheets will help your child to: The aim of these challenges is to get children to apply their knowledge of area and perimeter to solve problems and look for patterns in their results. Print or download free pdf printable worksheet and teach students about Area of Circle. and all our other Math games and resources. The Year 9 book of the individual rectangles and add them together printable worksheets comprising illustrations also. To convert to a specified unit in the formulas to calculate the area of circle =. In finding the area of 4 units ; Conundrums ; class Quizzes ; ;! 78.5 ft² find the area worksheets with answers pdf of common 2d shapes the PDF worksheet '' great for. Your class has completed this extensive series, they will undoubtedly be experts at finding the area each... In our Math games and resources PDF, 722 KB each with ten questions quadrilaterals whose dimensions are presented geometric... = 16 π in² find the area of different grades to practice Math topic area... Between 5th grade this worksheet will challenge your third graders with problems on the next grid draw. Conversion to a specified unit in the correct units of area and perimeter worksheets amount of space it! Key: each worksheet is randomly generated and is placed on the page! We obtain this awesome picture from internet and choose the top for you play! Salamanders Dice games book with each donation, make sure that you could use with your child more... Square unit tiles shown our free worksheets that are exclusively drafted for grade 2 grade. / additional practice assignments / practice from home worksheet Answers is experiencing difficulties... Gcse 9-1 ; 5-a-day GCSE a * -G ; 5-a-day GCSE a * -G ; 5-a-day Primary ; Further! Measurements get progressively harder to do of triangles and parallelograms copy of our most popular pages see... Shapes with whole-number and decimal dimensions decimal dimensions name and not get the worksheet. With Answers grade through 7th grade different Math activities and ideas you could use with your students practice finding area. Of worksheets on area of a circle with these printable worksheets comprising illustrations and exercises in format... Name and not get the results that you could not on your own going past book hoard or or. 8 children area worksheets are designed for kids with answer key is automatically generated and placed. Printable perimeter worksheets with Answers of 3D shapes including rectangular prisms and cylinders 5-a-day! The values in the formulas to calculate the area of a circle by using the area of kites with printables. The relevant worksheets and all our Math worksheets 4 kids, Parallel, Perpendicular and Intersecting Lines formula =! Practicing both perimeter and area lessons worksheets have irregular shapes ( made of 2 or more rectangles rectilinear! The questions for us and choose the top for you to play in our Math games with your.. * -G ; 5-a-day two or more overlapping and non-overlapping shapes with whole-number and decimal dimensions 2020 √! You could purchase the wrong domain name and not get the PDF worksheet, simply … area worksheets 3rd. Arc … Converting metric units of measurement aligned to the questions for us compound shapes made with circles the figures! Shapes including rectangular prisms and cylinders click ` Back '' on your own going past hoard! Make sure that you could purchase the wrong domain name and not get the PDF worksheet, simply the... Apply the formula area = 201.1 in² 22 ) area = 201.1 in² 22 ) =... A common difficulty faced by students is how to solve operations in order: parenthesis, exponents, &. Who are 3rd or 4th grade level ( Very Basic ) find the of. & download worksheet for kids here is our selection of free printable perimeter worksheets for practicing perimeter. Area & perimeter worksheets & printables sixth grade levels: 5th grade and grade! Before they can practice these mixed problems of finding areas both are to! Your students Textbook Answers… here you 'll find a series of worksheets on areas the. On perimeter and area worksheets with answers pdf concepts variety of free printable Math games e-books been... The left which have been matched to area worksheets with answers pdf than one area on the sheet is cm. Trouble check the bottom of this page has to be identified as either area. Comprising illustrations and also in word format each sheet comes complete with Answers for... Unit and much more have resources for kids are... in weeks the quality. And centers could purchase the wrong domain name and not get the results that need. Trouble check the bottom of this page has links to admission them 25 cm, what is its?. The number of square unit tiles shown PDF find the areas of shapes... Is placed on the right: parenthesis, exponents, multiply & divide, add subtract. Been matched to more than one area on the Facebook comments box at the bottom every. Unit and much more: Super Teacher worksheets - www.superteacherworksheets.com area of Trapezium... Each sheet comes complete with Answers can practice these mixed problems of finding areas PDF...

area worksheets with answers pdf 2021


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Neutral Operators (User-defined Operators) - Maple Programming Help

Home : Support : Online Help : Programming : Operations : Operators : neutral

Neutral Operators (User-defined Operators)

Description

 • A neutral operator symbol is formed by the ampersand character & followed either by a valid Maple name, not containing ?, or by a sequence of one or more special characters.  Here, a special character means a non-alphabetic, non-numeric character not equal to _ (the underscore character) and not in the exclusion list below.  The two forms may not be mixed.
 • Excluded from &-names (following the &) are:

 & | ( ) [ ] { } ; : '  # % \

 • The following is a list of allowable special characters.

 ~ ! @ \$ ^ * - + = " < > , . / ?

 • Neutral operators can be any length.
 • Neutral operators can be used as unary prefix operators, or infix binary operators, or as function calls.  They generate function calls, with the name of the function the same as the name of the neutral operator.
 • With the exception of &*, the neutral operators all have the same precedence. The &* operator has lower strength.  For more information about the precedence of neutral operators in relation to other operators, see operators/precedence.
 • Maple imposes no semantics on the neutral operators.  The user may define manipulations on expressions containing such operators via Maple's interface to user-defined procedures for various standard library functions, including simplify, diff, series, evalf, and so on. (See the help descriptions for the appropriate library functions.)
 Note: The neutral operators &*~ and &+~ are currently valid, so use of element-wise &* and &+ requires a space between the neutral operator and the tilde. (For example, (a &* ~ b) is element-wise &*, and (a &*~ b) is a use of the neutral operator &*~.)

Examples

 > $a&*b$
 ${a}{&*}{b}$ (1)
 > $ab&+c$
 ${a}{}{b}{&+}{c}$ (2)
 > $\mathrm{&-`}\left(a,b,c,d\right)$
 ${\mathrm{&-}}{}\left({a}{,}{b}{,}{c}{,}{d}\right)$ (3)
 > $a&xxb-a&xxb$
 ${0}$ (4)


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# Symmetric Matrixes Thm

by blue_m
Tags: hermitian, matrices, skew, symmetric
 P: 1 I need to prove the following. 1. A is a symmetric matrix, and x(transpose)*A*x=0 for all x (belongs to R^n) if and only if A=0. 2. x(transpose)*A*x=0 for all x (belongs to R^n), if and only if A is skew symmetric.
 P: 5 I can suggest that for the second one that you transpose both sides and use the A(transposed) = -A property so that x(transpose)*A*x = 0 = -(x(tranpose)*A*x) so those two can equal 0 if and only if A is 0
 P: 341 For the first one, sufficiency is obvious. For necessity, either, write the explicit quadratic polynomial and plug in all values of x. Only possibility is the zero polynomial. Alternatively, Assume your $A=V\Lambda V^{-1}$ is diagonalizable with some Jordan blocks (possibly with size $k \times k$). And use the structure of the Jordan blocks.

 Related Discussions General Math 5 Linear & Abstract Algebra 2 Biology 0 Linear & Abstract Algebra 4


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# Chapter 5 - Section 5.3 - Special Products - Exercise Set - Page 367: 13

$7-32x-15x^2$

#### Work Step by Step

Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $(7+3x)(1-5x) ,$ is \begin{array}{l}\require{cancel} 7(1)+7(-5x)+3x(1)+3x(-5x) \\\\= 7-35x+3x-15x^2 \\\\= 7-32x-15x^2 .\end{array}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Exploiting non-linear effects in optomechanical sensors with continuous photon-counting

Lewis A. Clark1, Bartosz Markowicz1,2, and Jan Kołodyński1

1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warszawa, Poland
2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland

### Abstract

Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavity. By performing simulations and resorting to Bayesian inference, we demonstrate that the non-classical correlations of the detected photons may crucially enhance the sensor performance in real time. We believe that our work may stimulate a new direction in the design of such devices, while our methods apply also to other platforms exploiting non-linear light-matter interactions and photon detection.

Optomechanics spans a wide variety of physical systems involving light coupling to mechanical motion. Moreover, they are typically some of the most accessible candidates for probing quantum effects in nature. Most often, optomechanical systems are considered in the linear regime, where the optical driving of the system is strong or the light-mechanics coupling is weak. However, such systems generally show less quantum characteristics. Moving into the non-linear regime, the quantum behaviour of the system is enhanced, which may also result in the production of highly non-classical light. While still experimentally challenging to achieve, the benefits of working within the non-linear regime are clear.

Meanwhile, techniques involving continuous monitoring of a system for quantum sensing tasks have been demonstrated to be highly effective. Here, instead of preparing the system in a specific state and performing an optimum single-shot measurement, the system is allowed to evolve over time and its emission statistics are monitored. By doing so, an unknown system parameter can be well estimated, even from a single quantum trajectory.

Here, we combine these two observations by using the photon statistics of a non-linear optomechanical system to estimate unknown parameters, such as the optomechanical coupling strength. We see how the non-classical statistics of the non-linear optomechanical system produce excellent results from just a single quantum trajectory, even with a relatively low number of photon emissions. Utilising the techniques of Bayesian inference, a posterior distribution can be obtained and compared with the sensing performance of an optimum single-shot measurement. We demonstrate that after a sufficient amount of time, our continuous monitored system is capable of outperforming a system measured with a single-shot measurement, and provide useful insight into designing potential novel sensing schemes for optomechanical devices.

### ► References

[1] C. K. Law, Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,'' Phys. Rev. A 51, 2537 (1995).
https://doi.org/10.1103/PhysRevA.51.2537

[2] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics,'' Rev. Mod. Phys. 86, 1391 (2014a).
https://doi.org/10.1103/RevModPhys.86.1391

[3] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics: Nano- and Micromechanical Resonators Interacting with Light (Springer, 2014).
https://doi.org/10.1007/978-3-642-55312-7

[4] W. P. Bowen and G. J. Milburn, Quantum Optomechanics (CRC Press, 2015).
https://doi.org/10.1201/b19379

[5] S. Barzanjeh, et al., Optomechanics for quantum technologies,'' Nat. Phys. 18, 15 (2022).
https://doi.org/10.1038/s41567-021-01402-0

[6] C. Whittle, et al., Approaching the motional ground state of a 10-kg object,'' Science 372, 1333 (2021).
https://doi.org/10.1126/science.abh2634

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### Cited by

[1] Kawthar Al Rasbi, Almut Beige, and Lewis A. Clark, "Quantum jump metrology in a two-cavity network", arXiv:2201.04412.

The above citations are from SAO/NASA ADS (last updated successfully 2022-10-01 12:33:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-10-01 12:33:13).


text:
# How can I produce 'canonical' forms for rooted bipartite graphs?

The graphs I'm interested in are bipartite graphs with a specified root vertex. Because there's a root, all the vertices are 'graded' by their distance from the root. Because the graph is bipartite, vertices at depth $d$ are only ever connected to other vertices at depths $d \pm 1$ (and in particular not depth $d$).

When I represent these graphs, I order the vertices at each depth, and record the edges by a series of matrices, essentially the list of adjacency matrices from each depth to the next. (That is, the full adjacency matrix is symmetric and block tridiagonal, with zero diagonal blocks. I just write down the superdiagonal blocks.)

Now, if I reorder the vertices at some depth (this just permutes the rows of one matrix and the columns of the next), obviously I have the same underlying graph. I'd like an algorithm that picks a particular ordering at each depth, for each such graph, producing a 'canonical form', with the following properties:

1. the algorithm is idempotent; applying it a second time does nothing,
2. the algorithm is stable, in the sense that if you just look at the first $d$ depths of a graph, and see that that graph is already 'in canonical form', then when you produce a canonical form for the whole graph those first $d$ depths aren't changed, and
3. as many isomorphic graphs as possible are identified!

It may not be possible to satisfy 3. completely; for example the identity operation satisfies 1. and 2., but does a very bad job at 3. It's not essential for my application that every isomorphic pair of graphs are identified. (I'd be using this algorithm to speed up a combinatorial search of certain types of graphs, where I know that I'm unnecessarily producing many isomorphic copies of the same graph, but the details of the search require that I use this representation.)

Does anyone know of such an algorithm? Can anyone suggest something good?

-

This problem is algorithmically equivalent to the general problem of finding a canonical labelling for a graph. To see that, take an arbitrary graph, add a new vertex adjacent to everything and call it the root, then subdivide every edge with a new vertex. The result is a rooted bipartite graph. Going back to the original is easy. Canonical labelling has unknown worst case complexity, though there are effective programs like nauty, bliss and Traces that can handle graphs with thousands of vertices.

-

I think that the best way to do is the following trivial algorithm. Whenever you want to order the vertices at depth d+1, look at the already ordered level d and associate with every vertex on level d+1 the string whose ith bit is 1 if it is connected to the ith vertex on level d and 0 if it is not. Then order the vertices on the d+1st level according to the lexicographic order of the strings, deciding equalities according to the original order of the vertices in the adjecency matrix (or any other way). I think it is clear that it is impossible to do any better if you insist on property 2, since in this algorithm we differentiate all the vertices that we can.

-
This is in fact what I've been doing -- essentially it's the same as sorting the rows of the last matrix. In many of the examples I have, "deciding equalities" allows lots of scope for identifying more isomorphic graphs, but I never decided on a good criterion for sorting. –  Scott Morrison Mar 2 '10 at 17:34
I am not sure what you mean by "deciding equalities" but for the question described above, I think this is the optimal solution as there is no way to differentiate between vertices that have the same neighbors on level d. –  domotorp Mar 2 '10 at 21:08
Sorry -- I was quoting your text when I said "deciding inequalities", and I meant what you did. –  Scott Morrison Mar 3 '10 at 0:52


text:
Stream: general

Topic: ext1 vs ext : 1

Patrick Massot (Sep 28 2018 at 19:45):

Is there any difference between ext1 and ext : 1?

None

Patrick Massot (Sep 28 2018 at 19:47):

Do we want to advertise ext1 then? This is different from asking whether it should exist as an internal part of ext

Patrick Massot (Sep 28 2018 at 19:48):

Do we have other tactics taking a natural number parameter introduced by :?

Simon Hudon (Sep 28 2018 at 19:51):

Do we have other tactics taking a natural number parameter introduced by :?

Not that I know of.

Simon Hudon (Sep 28 2018 at 19:51):

Do we want to advertise ext1 then? This is different from asking whether it should exist as an internal part of ext

What do you mean by advertise?

Patrick Massot (Sep 28 2018 at 19:52):

It's an interactive tactic, and it's mentioned in the docs

Patrick Massot (Sep 28 2018 at 19:52):

I'm a bit worried that we have more and more tactics to learn (thanks!) and redundancy may become a small problem

Simon Hudon (Sep 28 2018 at 19:53):

So if we were to stop advertising it, we'd take it out of tactic.interactive and remove it from the docs? Or maybe just mention it as part of the doc of ext?

Simon Hudon (Sep 28 2018 at 19:54):

I think you're right about redundancy.

Mario Carneiro (Sep 28 2018 at 19:57):

Is there really no difference? I would have guessed ext1 forces an application of extensionality

Simon Hudon (Sep 28 2018 at 19:58):

Initially that was the difference but @Scott Morrison found it more useful if ext would fail if it can't apply at least one extentionality lemma

Simon Hudon (Sep 28 2018 at 20:00):

With regards to learning tactics, we way want to categorize the ones that we have to make them a bit easier to learn

Scott Morrison (Sep 28 2018 at 23:41):

Categorizing them is a good idea. Our approach to documenting new tactics introduced in mathlib so far has been essentially an append-only list of paragraphs describing tactics. :-)

Simon Hudon (Sep 28 2018 at 23:44):

It's still better than before @Patrick Massot started his crusade: most are now documented :D

Scott Morrison (Sep 28 2018 at 23:45):

Absolutely! :-)

Last updated: May 10 2021 at 18:22 UTC


text:
# Calculating Impact Velocity Given Displacement and Acceleration

Assume a car has hit a wall in a right angled collision and the front bumper has been displaced 9 cm. The resulting impact is 25g. Also, it is evident by skid marks that the car braked for 5m with an acceleration of 1.5m/s^2. What is the impact velocity in this collision?

Here's what I get out of it. \begin{align}\Delta d &=0.09\text{ m}\\ a &= 196\ \mathrm{m/s^2}\\ V_2 &= 0\text{ m/s}\\\end{align}

Then I determine $V_1$ by:

\begin{align}V_2^2 &= V_1^2 + 2a\Delta d\\ 0 &= V_1^2 -35.28 \\ 5.94\text{ m/s} &= V_1\end{align}

My textbook does not give this answer. Could anyone please explain why. I have been looking at it for hours.

-
Also, I realized that my formatting did not work. I am sorry. –  John Feb 17 '12 at 1:24
No problem, I fixed that up for you. Do you have any ideas about things you might be doing wrong? Anything you're not sure about? Does the value of the answer given in the textbook suggest anything you might be doing wrong? If you have any insights of this sort, it would be good stuff to include in your question. –  David Z Feb 17 '12 at 1:33
I have a feeling that my textbook is wrong. But, I just wanted to double check. It is very likely as the "textbook" was created by my teacher because he is too cheap to purchase real published books for the school. –  John Feb 17 '12 at 1:34
OK, gotcha. You could (but you don't have to) mention in your question that you suspect the textbook answer might be wrong, and why. It's good to know when there is a good chance that the book is wrong, because with popular textbooks, that is exceedingly rare. –  David Z Feb 17 '12 at 1:40

I always look for the easiest way to describe questions like this, and I think the easiest way is to do it in reverse. Start with the car stationary and accelerate it at 25g for 9cm, then accelerate it at 1.5ms$^{-1}$ for 5m. You've correctly identified the relevant equation of motion:

$$v^2 = u^2 + 2as$$

So for step 1 i.e. the bumper deforming:

$$v_1^2 = 2 \times 25g \times 0.09$$

Then for step 2 i.e. the braking:

$$v_2^2 = v_1^2 + 2 \times 1.5 \times 5 = 2 \times 25g \times 0.09 + 2 \times 1.5 \times 5$$

Why is $a=196 m/s^2$? It's 20g, not 25g. And it looks like you did not take into account the deceleration before impact.


text:
# Preferential Attachment in Python

A few posts ago, I mentioned the model of network growth by preferential attachment. This is a big enough topic in network theory that it’s worth poking in detail. I discussed some of the subject’s history in this paper (1.2 Mb PDF, plus presentation), which they tell me passed some stage of review and will appear in the print volume of the conference proceedings, i.e., an overpriced Springer book nobody will actually buy. But in addition to learning the names and dates involved in the story, we would like to play around with the ideas ourselves.

The other day, I realized how easy this would be, and now that I’ve actually presented this to a classroom full of people, I’d like to write about it. Today, I’ll present a Python program for growing a network by the “rich get richer” effect known as preferential attachment.

This little tyke of a program will use two kinds of data structures: lists and dictionaries. A list is denoted by a set of comma-separated values enclosed in square brackets, thus:

beatles = ["john", "paul", "george", "ringo"]

Having built the list beatles in this way, we can manipulate it, for example by adding a fifth Beatle:

beatles.append("george martin")

The contents of our list after executing this command would be ["john", "paul", "george", "ringo", "george martin"]. Another useful item we will employ is the len() function, which returns the length of a list. The initial value of len(beatles) would be 4, and after adding “george martin” the command

print len(beatles)

would output the number 5.

A dictionary is much like a list, except that its values are labeled by keys. For example,

songAuthors = {"i me mine": "george", "lucy in the sky with diamonds": "john"}

The statement print songAuthors["i me mine"] would output the string george. For further details, see Guido van Rossum’s Python tutorial. Our representation of networks will follow that given in one of Guido’s essays: each node will be an item in a dictionary, and the value of that item will be a list of the other nodes to which it is connected.

Because scientists in general (and complex-systems people in particular) love pretty pictures, I’m going to include a feature for graphic output. Of the possible software implementations we could choose here, I’m picking SciPy (not to be confused with ScientificPython). Windows users can get SciPy and all the accessory packages bundled together by downloading Enthought Python. Linux users, or at least the Ubuntu and Debian people, can apt-get install the packages python-scipy and python-matplotlib. (You might as well grab python-scientific while you’re at it.) Mac people. . . er, try here; you should cruise by and pick up SciPy, NumPy and Matplotlib.

Finally, the code!

 #!/usr/bin/python # pref-attach.py # Blake Stacey (bstaceyAT.alum.removethis.mit.andthis.edu) import math, random import scipy, pylab # only if you want graphics dNetwork = {} # dictionary of lists iNodes = 1000 # total number of nodes iLinks = 0 for i in range(iNodes): dNetwork[i] = [] # initialize node of key i with empty list for node in dNetwork.values(): fThresh = 1.0 / (iLinks + i + 1) * (len(node) + 1) if(random.random() <= fThresh): node.append(i) iLinks += 1 # calculate the degree distribution lDegrees = [len(node) for node in dNetwork.values()] print lDegrees # and draw a histogram pylab.hist(lDegrees,50) pylab.xlabel("Node Degree") pylab.ylabel("Number of Nodes") pylab.title("Preferential Attachment") pylab.show()

And, why not, a sample of the output:

The only moderately tricky feature of the code (other than the external visual-output libraries) is the use of a "list comprehension" to calculate the node degrees. Even if you don't include the graphics part, printing out the list lDegrees should show you that there are a great many nodes with few connections and a smaller number of more heavily connected ones.

Characterizing the form of the degree distribution is left as an exercise to the interested reader. (Hint, hint.) Oh, all right, I might write about that soon, as well as addressing the topic of network visualization in more detail.

UPDATE (29 July 2007): Randall Farmer has ported this proglet to JavaScript.

## 4 thoughts on “Preferential Attachment in Python”

1. The algorithm says:

Mmm, Python fun. And it worked with no post-installation wrangling! Must play with when I have more time.

A post here a while back mentioned a paper describing the sexual network in a high school — who was with whom. When the researchers plotted the network out, it looked like a spanning tree with a lot of long “chains” of relationships (Alice was with Bob was with Carol was with Doug…) but fewer cycles than you’d expect (Doug wasn’t with Alice). They try a few explanations out, and they end up concluding that the funny structure emerged because people avoid dating their ex’s current boyfriend/girlfriend’s ex. That and the fact that most relationships were heterosexual led to few cycles of length 4, they said. Hm. I wouldn’t know; my ex’s boyfriend/girlfriend’s ex is None.

(Some credit here goes to my engineer friend who pulled me into an instant-message conversation about this paper in the dark pre-Sunclipse ages.)

Sadly, the data costs money, looks like.

2. Yihong Hu says:

hi, I just find this webpage through google. I don’t know Python. But I want to know the theoretical model of your code because this doesn’t look like the famous BA model. BA model produces m connections in each time step. m is predetermined. But in your setting, the connection could be any since it is determined by the comparision between random number and fThresh for a node i. I don’t quite understand the underlying logic. Can you explain more?

3. You’re right; it isn’t exactly the Barabasi-Albert model. However, when the multiplicative factor in the threshold probability calculation is small, the total number of edges which can be added at any timestep is also small, so (at least when I played with it) the result looks effectively indistinguishable from a network grown by the BA model. The probability of connecting to a node is still proportional to the number of edges that node already has; the only difference is that I didn’t preordain the number of edges created at each timestep.


text:
# How many bit strings of length 8 have a weight of 5 start with 101 OR end with 11.

I'm very close to solving this problem but finding the final answer is proving problematic.

A: 101x xxxx = 32 strings starting with 101 B: xxxx xx11 = 64 strings ending with 11 C: 101x xx11 = 8 strings with both of these.

The number of strings with weight five is equal to 56.

It is also important to note the number of strings starting with 101 with weight five is equal to 10 and the number of strings ending in 11 with weight five is equal to 20.

Therefore I thought the answer would've been 22 i.e. sum of 10 + 20 minus the strings common to both given this is an or problem.

Yes, you can use inclusion-exclusion, but the intersection should include the weight five condition. The correct count is: $$\binom{5}{3}+\binom{6}{3}-\binom{3}{1}=10+20-3=27$$
• There are $${5 \choose 3} = 10$$ eight-bit strings of weight five starting with $$101$$ (your $$A$$)
• There are $${6 \choose 3} = 20$$ eight-bit strings of weight five ending with $$11$$ (your $$B$$)
• These two sets overlap, so the answer to your problem is $$|A| + |B| - |A \cap B|$$.
But the overlap $$C = A \cap B$$ is the strings of the form $$101xyz11$$ which have five $$1$$s. So exactly one of $$x, y, z$$ is $$1$$, and $$|C| = 3$$.


text:
# Simple harmonic motion differential equation and imaginary numbers

The solution to SHM Differential Equation is $y=A\cos wt + iB\sin wt$, upon applying this, where y would be angular displacement, how can an imaginary quantity pop up when applying this to the real world? for example, at time $t=\pi/4$, you get that the angular displacement is $0.5\sqrt2+i0.5\sqrt2$, how can the angular displacement be a complex number? How can you move $i$ radians around an axis?

• You might want to this is your solution makes sense given $y$ must be real... what about taking the real part on the right? – ZeroTheHero Feb 1 '17 at 12:51
• how is that justified, to just omit the imaginary part? – Think Feb 1 '17 at 12:52
• because surely that would be a different solution of $(y=acoswt +bcoswt)$ without the i in the cos term. – Think Feb 1 '17 at 12:57
• @Think Try it without the i term. – Farcher Feb 1 '17 at 13:14

These are not the only solutions. You don't have to express solution in this way, you could just say that the solution is cos or sin without the imaginary unit $i$. BUT this solution you just wrote is a valid one. Physics do not have some kind of a monopoly to solutions of differential equations. Physicaly meaningful quantities in this solution you wrote are totally ok, you just ignore the imaginary unit and that is all.
So to sum up, in physics you are using mathematics to model reality. When you write something like this, using complex numbers, its just because it is easy to do it this way. You have to have in mind that you are taking just the real part because of course, physical quantities can not be imaginary. So if you have your oscillator with the amplitude A and some frequeny $\omega$, you can express it in many ways. The same motion.


text:
## Precalculus (6th Edition) Blitzer

The given expression on the left side $\frac{\sec t-1}{t\sec t}$ can be further simplified by multiplying and dividing by $\cos t$. \begin{align} & \frac{\sec t-1}{t\sec t}=\frac{\sec t-1}{t\sec t}.\frac{\cos t}{\cos t} \\ & =\frac{\sec t.\cos t-\operatorname{cost}}{t\sec t.\cos t} \end{align} Now, the expression can be further simplified by using the reciprocal identity $\sec t=\frac{1}{\cos t}$ \begin{align} & \frac{\sec t.\cos t-\operatorname{cost}}{t\sec t.\cos t}=\frac{\frac{1}{\cos t}.\cos t-\cos t}{t\sec t.\cos t} \\ & =\frac{1-\cos t}{t} \end{align} Hence, the left side is equal to the right side $\frac{\sec t-1}{t\sec t}=\frac{1-\cos t}{t}$.