Without using a calculator, explain why the solution to each equation must be a real number between 1 and 2.

Mathematics

1 answer:

kondor19780726 [428]3 years ago

8 0

Explanation:

The intermediate value theorem (IVT) tells you that for continuous function ...

f(x) = 11^x

if f(1) < 12 and f(2) > 12, then for f(x) = 12, the value of x must be between 1 and 2.

We know f(1) = 11^1 = 11 < 12, and f(2) = 11^2 = 121 > 12, so the conditions are met for the IVT to be applicable.

In short, the Intermediate Value Theorem says so.

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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

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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