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3 years ago

Help. I forgot how to do this please

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

5 0

Answer:

176 in³

Step-by-step explanation:

Area is a 2-dimensional measure, so the scale factor for area of similar figures is the 2nd power of the linear scale factor. That is, the ratio of linear dimensions of the two figures is ...

smaller/larger = √(228/1425) = √(4/25) = 2/5 . . . . linear scale factor

Volume is a 3-dimensional measure, so the scale factor for volume of similar figures is the 3rd power of the linear scale factor. That is, the ratio of volumes of the two figures is ...

smaller/larger = (2/5)^3 = 8/125 . . . . . . . . volume scale factor

Multiplying this by the larger volume gives us the smaller volume:

(8/125)·(2750 in³) = 176 in³

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Step-by-step explanation:

we want to solve the following trigonometric equation:

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The first step of solving trigonometric equation is to rewrite the equation in terms of one trigonometric function . With Pythagorean theorem, we know that sin²x=1-cos²x . It will be helpful to rewrite the equation in terms of one trig functions. Therefore, substitute 1-cos² $\theta$ in the place of sin² $\theta$ :

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back-substitute:

$\begin{cases} \cos( \theta) = \dfrac{1}{2} \\ \cos( \theta) = - 1 \end{cases} \theta \in[0,2\pi)$

take inverse trig in both sides

$\implies \begin{cases} \theta = \dfrac{\pi}{3} + 2n\pi\\\theta= \frac{5\pi}{3} + 2n\pi \\ \theta = \pi + 2n\pi\end{cases} \theta \in[0,2\pi) \\\\\implies\theta= \frac{\pi}{3}+\dfrac{2n\pi}{3},\theta\in [0,2\pi)\\\text{when n=0}\\ \implies \theta = \frac{\pi}{3} \\ \text{when n=1}\\ \theta= \pi\\ \text{when n=2}\\\theta=\frac{5\pi}{ 3}$

In conclusion,

$\displaystyle\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}$

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