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2 years ago

9

You and three friends go to the local fair. You each buy a $3 food ticket and a stamp for unlimited rides. If the total cost for

the four of you is $32, how much does the stamp for unlimited rides cost?

1 answer:

ikadub [295]2 years ago

3 0

Answer:

its should be 23

because

3x3 is 9

9+23=32

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Unless otherwise posted, what is the speed limit in a residential area?

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Residential speed limit is 40 mph unless otherwise posted. Residential speed limit is 30 mph unless otherwise posted.

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3 years ago

The perimeter of a sector of a circle of radius 21cm is 64cm,find the angle of the sector

Alla [95]

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The angle is 60 degrees

Step-by-step explanation:

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3 years ago

Which of the following expressions is equivalent to 13^(2)-3^(2)

Amiraneli [1.4K]

Answer:

160

Step-by-step explanation:

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2 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

The aspect ratio of a TV screen is the ratio of the width to the height of the image. A regular TV has an aspect ratio of 16: 9.

ki77a [65]

Answer:

Width = 44.45 inches

Height = 25.00 inches

Step-by-step explanation:

(16x)^2 + (9x)^2 = 51^2

256x^2 + 81x^2 = 2601

337x^2 = 2601

x^2 = 7.718

x = 2.778

Width = 44.45 inches

Height = 25.00 inches

I think this is right

7 0

4 years ago