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2 years ago

9

Point A is located at (-5, 2) on a coordinate grid. Point A is translated 4 units to the right and 2 units down to create point

A.
Which measurement is closest to the distance between point A and point A' in units?
A)
4.1 units
B)
4.3 units
o
4.5 units
D)
4.7 units
We

1 answer:

HACTEHA [7]2 years ago

3 0

The correct solution is A thanks

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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

PLEASE HELP ME AND PLEASE BE RIGHT I ALREADY HAVE AN 80 :(

ELEN [110]

Answer:

D

Step-by-step explanation:

When calculating the area of a parallelogram, use the formula A = l*h where length is the longest length and h is the perpendicular height of the shape. For this parallelogram, substitute l = 14 and h = 8.

A = l*w = 14*8 = 112

6 0

3 years ago

1/3(3x - 12) = x - 4

PIT_PIT [208]

Step-by-step explanation:

the formula is too long so the link is below:

https://www.geteasysoloution.com/1/3x+12=x-4

3 0

3 years ago

PLEASE HELP! :)

Katarina [22]

Well lets see. You have a total of 52 marbles. So all you would have to do would be to find the percent of 52 out of 60. This sounds confusing and I may not be completely right but I hope you give it a shot!

3 0

3 years ago

Whats is 32 plus 45 minus 6

kondor19780726 [428]

32 plus 45 minus 6

= 32 + 45 - 6

= 71

3 0

3 years ago

Read 2 more answers