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3 years ago

15

On a map, 1 inch equals 15 miles. Two cities are 2 inches apart on the map. What is the actual distance between the cities?

1 answer:

BabaBlast [244]3 years ago

4 0

Since the scale is 15 miles per inch all you need to do is multiply.
2in(15)=30
The cities are 30 miles apart.

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How much interest is earned on $470 at 4% for 36 months?

bulgar [2K]

Answer:

The interest earned on $470 at 4% for 36 months is $56.4

Step-by-step explanation:

We are given

Principal Amount P₀= $470

Rate r = 4% = 0.04

Time t = 36 months = 3 years

We need to find interest I

The formula used is: $I=P_ort$

Putting values and finding Interest I

$I=P_ort\\I=470(0.04)(3)\\I=56.4$

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3 years ago

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Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

$\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}$

Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

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$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

$\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta$

$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

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$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }$

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$\sin \beta=\frac{1}{\sqrt{2} }$ or $\sin \beta=-\frac{2}{\sqrt{2} }$

$\sin \beta=\frac{\sqrt{2}}{2}$ or $\sin \beta=-\sqrt{2}$

When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

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3 years ago

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Answer

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Answer:

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Step-by-step explanation:

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4 years ago

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