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2 years ago

13

brady has a card collection with 64 basketball cards, 32 football cards, and 24 baseball cards. he wants to arrange the cards in

equal piles, with only one type of card in each pile. how many cards can he put in each pile?

1 answer:

inysia [295]2 years ago

8 0

The answer=24 that he needs to put in each pile

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A number to the 12th power divided by the same number to the 9th power equals 125 what is the number

nadezda [96]

If x to the 12th power is divided by x to the 9th power:

Since they share same bases, and are being divided, it would be the same as x^{12 - 9), or x^{3}

Now, simply find the cube root of 125, which is 5.

Therefore, the number (x) must be equal to 5.

<em>Hope this helps! :)</em>

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3 years ago

sasho [114]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 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