What this simplified

Mathematics

1 answer:

kati45 [8]2 years ago

5 0

Answer:

$\frac{3b\sqrt[3]{c^{2}} }{a^{2} }$

Step-by-step explanation:

∛(27a⁻⁶b³c²)

To simplify, first apply the cube root the each of the terms. Keep in mind this rule: $\sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m} = a^{m/n}$

∛27 = 3 (because 3*3*3 = 27)

∛a⁻⁶ = $a^{-6/3}$ = $a^{-2}$ = $\frac{1}{a^{2}}$

∛b³ = $b^{3/3}$ = $b^{1}$ = b

∛c² = $c^{2/3}$

∛(27a⁻⁶b³c²)

= $\frac{3b\sqrt[3]{c^{2}} }{a^{2} }$

Simplified form generally follows these rules:

No negative exponents

No fraction exponents

Keep in fractional form

Reduce numerical values

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If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building ro

maksim [4K]

SOLUTION

Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

$\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}$

So we have

$\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}$

Hence the answer is 104.9 feet to the nearest tenth