How do I solve for f of f

Mathematics

1 answer:

KengaRu [80]3 years ago

8 0

Answer:

$\large\boxed{(F\circ F)(n)=4n+6}$

Step-by-step explanation:

$F(n)=2n+2\\\\(F\circ F)(n)\to\text{Replace n with 2n + 2 in F(n)}:\\\\(F\circ F)(n)=2(2n+2)+2\qquad\text{use the distributive property}\\\\(F\circ F)(n)=(2)(2n)+(2)(2)+2=4n+4+2=4n+6$

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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