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4 years ago

Assume there is a cube with all sides equal to x. The change in x with respect to t is x(t)=2t. What is the formula for the rate

of change of the volume of the cube?

Mathematics

1 answer:

yarga [219]4 years ago

6 0

$\bf \textit{volume of a cube}\\\\ V=x^3~~ \begin{cases} x=length~of\\ \qquad a~side\\[-0.5em] \hrulefill\\ x(t)=2t\\ x=2t \end{cases}\implies V=[x(t)]^3\implies V=[2t]^3 \\\\\\ V=[2^3t^3]\implies V=8t^3\implies \boxed{\cfrac{dV}{dt}=24t^2}$

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Digiron [165]

Answer:

The mean of the random variable is 0.

The variance of the random variable is $\frac{3}{2}$

Step-by-step explanation:

We are given the following probability distribution:

$P(X = -2) = \frac{1}{8}$

$P(X = -1) = \frac{2}{8}$

$P(X = 0) = \frac{2}{8}$

$P(X = 1) = \frac{2}{8}$

$P(X = 2) = \frac{1}{8}$

Mean:

Sum of each value multiplied by its probabilities. So

$E(X) = -2\frac{1}{8} -1\frac{2}{8} + 0\frac{2}{8} + 1\frac{2}{8} + 2\frac{1}{8} = \frac{-2 -1 0 + 1 + 2}{8} = \frac{0}{8} = 0$

The mean of the random variable is 0.

Variance:

Sum of the difference squared between each value and the mean, multiplied by its probabilities. So

$V(X) = \frac{1}{8}(-2-0)^2 +\frac{2}{8}(-1-0)^2 + \frac{2}{8}(0-0)^2 + \frac{2}{8}(1-0)^2 + \frac{1}{8}(2-0)^2 = \frac{4 + 2 + 0 + 2 + 4} = \frac{12}{8} = \frac{3}{2}$

The variance of the random variable is $\frac{3}{2}$

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3 years ago

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Shalnov [3]

40.8/8= just simply divide

40.8/8= 5.1

Now let's check

8*5.1= 40.8 so that's the correct answer!

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