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3 years ago

A park is four times as long as it is wide. If the distance around the park is 12.5 km what is the area of the park?

Mathematics

1 answer:

Helen [10]3 years ago

7 0

Answer:

the area is 6.25 km^2

Step-by-step explanation:

1.25 = x

5 = 4x

1.25 * 5 = 6.25

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The scale drawing of a window is 1 inch by 2 inches. The actual size of the window is 24 inches by 48 inches.

weeeeeb [17]

This means that every 1 inch in the drawing is 24 inches of the actual size.

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3 years ago

it cost 270 for 3 people to go on a fishing trip how much does it cost for 10 people to go on the fishing trip

sdas [7]

270 divided by 3 = 90.

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2 years ago

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Step-by-step explanation:

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3 years ago

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Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$