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3 years ago

9

F the height remains fixed and the side of the base is decreasing by 0.002 meter/yr, what rate is the volume decreasing when the

height is 180 meters and the width is 200 meters?

1 answer:

katrin [286]3 years ago

4 0

The original volume equation looks like this: V = 1/3 * h * (x^2)
After the side is reduced by 0.002, the new volume would look like V1 = 1/3 * h * (x-0.002) ^ 2

Then we have:
V-V1 = 1/3*h*(x^2) - 1/3*h*(x – 0.002) ^2

= 1/3 * h *(x^2 - (x – 0.002) ^2)

= 1/3 * h * (0.004x - 0.00004)

The rate of decreasing is computed by:

(V-V1)/V * 100% = [1/3 * h *(0.004x - 0.00004)] / [1/3 * h * (x ^ 2)] * 100% this would be equal to (0.004x - 0.00004) / (x^2) * 100%

So replace x by 200, you’ll get:

(0.004(200) - 0.00004) / (200^2) * 100%

= 0.001999% is the rate of decreasing.

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Answer: False

Explanation:

$3x^2-12+12=0+12$

$3x^2=12$

$\frac{3x^2}{3}=\frac{12}{3}$

$x^2=4$

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$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

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Answer: True

Explanation:

$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

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Ths solutions for the equation 2(x-3)^3 - 18 = 0 are x = 6 and x = 0

Answer: False

Explanation:

$2\left(x-3\right)^3-18+18=0+18$

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$\frac{2\left(x-3\right)^3}{2}=\frac{18}{2}$

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$\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7

Answer: False

Explanation:

$2\left(x-5\right)^2-8+8=0+8$

$2\left(x-5\right)^2=8$

$\frac{2\left(x-5\right)^2}{2}=\frac{8}{2}$

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Answer: False

Explanation:

$\left(x+3\right)^2-25+25=-8+25$

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$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

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The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4

Answer: False

Explanation:

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Answer: False
Explanation:

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$\left(2x-1\right)^2=49$

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Answer: True
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$3\left(x+2\right)^2=3$

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Answer: True

Explanation:

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<u><em>~Lenvy~</em></u>

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