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lina2011 [118]
3 years ago
6

Which number is a common factor of 64 and 100? A) 4 B) 8 C) 16 D) 20

Mathematics
2 answers:
antiseptic1488 [7]3 years ago
5 0

Answer:

4

Step-by-step explanation:

Karolina [17]3 years ago
3 0

Answer:

A) 4

Step-by-step explanation:

The factors of 64 are:

1, 2, 4, 8, 16, 32, 64

The factors of 100 are:

1, 2, 4, 5, 10, 20, 25, 50, 100

The common factors are:

1, 2, 4

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3 years ago
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olya-2409 [2.1K]

Answer:

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7 0
2 years ago
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what are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x- pi) from x = 0 to x= 2 pi?
julsineya [31]

Answer:

\frac{\pi }{2} and \frac{3\pi }{2}

Step-by-step explanation:

To find the max points we need to take the derivative of the function and then find the critical values.

First we take the derivative:

f(x) = 4cos(2x-\pi )\\f'(x)=-4sin(2x-\pi )(2)\\f'(x)=-8sin(2x-\pi )\\

Now we need to find when f'(x)=0 to find the critical values.

0=-8sin(2x-\pi )\\0=sin(2x-\pi )\\sin^{-1}0=2x-\pi \\0=2x-\pi \\\pi =2x\\\frac{\pi }{2} =x

The critical values will be

\frac{\pi }{2} n for any integer n

between 0 and 2 pi, the critical values will be

0, \frac{\pi }{2} ,\pi ,\frac{3\pi }{2},2\pi

We can determine if these are minimums or maximums by using the second derivative test.

So we need to take the second derivative;

f'(x)=-8sin(2x-\pi )\\f''(x) = -8cos(2x-\pi )(2)\\f''(x)=-16cos(2x-\pi)

We need to see if the second derivative is positive or negative to determine if it is a max or min.

f''(0) = 16\\f''(\frac{\pi}{2})=-16\\f''(\pi )=16\\f''(\frac{2\pi}{3}) = -16\\

Since the second derivative is negative at

\frac{\pi }{2} and \frac{3\pi }{2}

we know both of those are the x-values of maximums.

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3 years ago
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