Compare 643251;633512;and 633893. the answer is 633251.

Mathematics

1 answer:

NeX [460]4 years ago

3 0

It is 1,277,144 I did it on the Calculator

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A ball has a volume of 128 cubic inches. Find the diameter of the ball.

Natalija [7]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
V=128
\end{cases}\implies 128=\cfrac{4\pi r^3}{3}\implies 128(3)=4\pi r^3$

$\bf \cfrac{128(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{128(3)}{4\pi }}=r^3\implies \sqrt[3]{\cfrac{96}{\pi }}=r\implies \sqrt[3]{\cfrac{8\cdot 12}{\pi }}=r
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\sqrt[3]{\cfrac{2^3\cdot 12}{\pi }}=r\implies 2\sqrt[3]{\cfrac{12}{\pi }}=r\\\\
-------------------------------\\\\
\textit{and since the diameter is \underline{twice as the radius}}\qquad d=4\sqrt[3]{\cfrac{12}{\pi }}$

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4 years ago

Find the dr/d(theta) for:<br>r = (theta)sin(theta) + cos(theta)

maxonik [38]

$r=\theta\sin\theta+\cos\theta$

$\dfrac{\mathrm dr}{\mathrm d\theta}=\dfrac{\mathrm d(\theta\sin\theta)}{\mathrm d\theta}+\dfrac{\mathrm d(\cos\theta)}{\mathrm d\theta}$

By the product rule,

$\dfrac{\mathrm d(\theta\sin\theta)}{\mathrm d\theta}=\dfrac{\mathrm d(\theta)}{\mathrm d\theta}\sin\theta+\theta\dfrac{\mathrm d(\sin\theta)}{\mathrm d\theta}=\sin\theta+\theta\cos\theta$