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Mathematics

1 answer:

sleet_krkn [62]2 years ago

4 0

Answer:

See below

Step-by-step explanation:

aⁿ = a×a×a×....×a (power n of the number a = number a multiplied by itself n times)

2^(10)= 2x...x2 how many times = 10 times 2

15^(57)= 15x...x15 how many times = 57 times 15

(-4)x...x(-4) 7 times = (-4)^(7)

(1.5)x...x(1.5) 12 times = (1.5)^(12)

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Robert buys 4 pounds of cauliflower at $0.85 a pound. He also buys 4 pounds of brussels sprouts. If he spends $6.40 on the veget

postnew [5]

$0.85 * 4 = $3.40

$6.40 - $3.40 = $300

Brussel sprouts per pound = $300 / 4
= $0.75

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3 years ago

Read 2 more answers

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.

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