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Ipatiy [6.2K]
2 years ago
15

The radius of a sphere is 12 units. Find the volume of the sphere. Write your answer in terms of pi.

Mathematics
1 answer:
stiv31 [10]2 years ago
5 0

Answer:

V = 2304π units³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = \frac{4}{3}πr³ ( where r is the radius ) , then

V = \frac{4}{3}π × 12³

   = \frac{4}{3} π × 1728

   = 4π × 576

   = 2304π units³

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Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total
Katarina [22]

Answer:

t-shirts: 2790

profit: $12209

Step-by-step explanation:

Given  the function:

p(x) = -x³ + 4x² + x

we want to maximize it.

The following criteria must be satisfied at the maximum:

dp/dx = 0

d²p/dx² < 0

dp/dx = -3x² + 8x + 1 = 0

Using quadratic formula:

x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}

x = \frac{-8 \pm \sqrt{8^2 -4(-3)(1)}}{2(-3)}

x = \frac{-8 \pm 8.72}{-6}

x_1 = \frac{-8 + 8.72}{-6}

x_1 = -0.12

x_2 = \frac{-8 - 8.72}{-6}

x_2 = 2.79

d²p/dx² = -6x + 8

d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0

d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0

Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.

Replacing into profit equation:

p(x) = -(2.79)³ + 4(2.79)² + 2.79 =  12.209

that is, $12209

3 0
3 years ago
7] A recent poll discovered that only 24.5% of Americans are getting the recommended amount of exercise per week. Briscoe Middle
Evgesh-ka [11]

Answer:

your TRASH NOOB LOSER

Step-by-step explanation:

so todya eat hesde

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3 years ago
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4 0
3 years ago
I’m a little confused
Vikki [24]
Hello lol

Answer:

(-1,-4)

Explanation:

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3 0
3 years ago
A rectangle has an area of 72 square inches. The width of the rectangle is 6 inches. What is the length of the rectangle?
inn [45]

Answer:

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Step-by-step explanation:


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