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3 years ago

5

On Monday, three hundred ninety - two students went on a trip to the zoo. All nine buses were filled and five students had to tr

avel in cars. How many students were in each bus ?

1 answer:

Vikki [24]3 years ago

5 0

The answer to your question is 43

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Point C has a _____ abscissa and a _____ ordinate.

bulgar [2K]

Abcissa is x, and ordinate is y.

In this case the x is positive, and the y is negative.

Therefore, the answer is "positive, negative"

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2 years ago

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Are there any integers between 0 and 1? Explain

zvonat [6]

Answer:

No

Step-by-step explanation:

Integers are whole numbers (not decimals or fractions) that are either <u>positive,</u> <u>negative</u>, or <u>zero</u>.

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3 years ago

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Angle I and N are complementary. If angle N has a meause of 48 degrees, find the measure of angle I

Afina-wow [57]

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42°

Step-by-step explanation:

Complementary angles are two angles that add up to 90°

1) 90-48 = 42

Hope this helps! :)

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3 years ago

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What is the sum of the polynomials? (6x+7x+x^2)+(2x^2-3x)

Trava [24]

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3x^2 + 10x

Step-by-step explanation:

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2 years ago

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:

$x = a\sin{\theta}$

So

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

In this question:

$a = 3$

$x = 3\sin{\theta}$

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

So

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

We have the following trigonometric identity:

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

So

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

Replacing into the integral:

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

Coming back to x:

We have that:

$x = 3\sin{\theta}$

So

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

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

8 0

2 years ago