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3 years ago

Which pyramids with base area B and height h have equal volumes.

Mathematics

1 answer:

Reptile [31]3 years ago

5 0

C and D

the volume ( V) of a pyramid is found using the formula

V = $\frac{1}{3}$ × area of base × height

calculating each of the volumes gives

(A) V = $\frac{1}{3}$ × 10.5 × 6 = 21 in³

(B) V = $\frac{1}{3}$ × 3.6 × 8 = 9.6 in³

(D) V = $\frac{1}{3}$ × 6 × 8.4 = 16.8 in³

C and D have equal volumes

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Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

<u>Second derivative test</u>

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

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3 years ago

Aisha mixes 50 milliliters of yogart, 100 grams of fruit and 250 milliliters of milk to make a smoothie what is the ratio of the

Aneli [31]

The ratio is of yogurt to fruit to milk is 1:2:5
Hope this helps! :D

5 0

3 years ago

Is my answer correct ??

qwelly [4]

Yessir, or at least as far as im concerned it looks like it

3 0

3 years ago

Micah is saving for a new skateboard. It costs $65, including tax. Micah has already saved $37. What in the equation?

RSB [31]

Answer:

x + 37 ≥ 65

Step-by-step explanation:

Given:

Money Micah wants = $65

Money Micah had = $37

Find:

Money Micah need

Computation:

Money Micah need(x)

x + 37 ≥ 65

So,

Money Micah need = 65 - 37

Money Micah need = $28

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3 years ago

What is the standard deviation for a normal distribution of the times of the first seven runners?

Ivahew [28]

We need specifics about the data

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3 years ago