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DENIUS [597]
2 years ago
15

Solve the right triangle. Round to the nearest degree and nearest tenth of a unit. What is the right angleV?

Mathematics
1 answer:
N76 [4]2 years ago
4 0

Answer:

  m∠V ≈ 61°

Step-by-step explanation:

The hypotenuse and the side opposite the angle of interest are given. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(V) = XW/XV = 7/8

The inverse sine function is used to find the angle:

  V = arcsin(7/8) ≈ 61°

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ANSWER

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EXPLANATION

We want to find the number of years that it will take the population to double.

To do this, we have to apply the exponential growth function:

y=a(1+r)^t

where y = final value

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r = rate of growth

t = time (in years)

For the population to double, it means that the final value must be 2 times the initial value:

y=2a

Substitute the given values into the function above:

\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}

To solve further, convert the function from an exponential function to a logarithmic function as follows:

\log _{1.08}2=t

Solve for t:

\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}

It will take 9 years for the population to double.

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Answer:

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Double-Check *******************

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Step-by-step explanation:


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