Mathematics
24.12.2020 03:48
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What is the rate of change for f(x)=-2cos4x-3 on the interval from x=0 to x=pi over

What is the rate of change for f(x)=-2cos4x-3 on the interval from x=0 to x=pi over 4
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christingle2004
christingle2004
4,8(44 marks)

\frac{16}{\pi}

Step-by-step explanation:

The average rate of a function f on interval x=a to x=b is:

\frac{f(b)-f(a)}{b-a}.

a=0 and b=\frac{\pi}{4} here for this problem where f(x)=-2\cos(4x)-3.

So we will need to evaluate f for x=0 \text{ and } b=\frac{\pi}{4}.

To find f(0) we will replace x in f(x)=-2\cos(4x)-3 with 0:

f(0)=-2\cos(4(0))-3

f(0)=-2\cos(0)-3

f(0)=-2(1)-3

f(0)=-2-3

f(0)=-5

To find f(\frac{\pi}{4}) we will replace x in f(x)=-2\cos(4x)-3 with \frac{\pi}{4}:

f(\frac{\pi}{4})=-2\cos(4(\frac{\pi}{4}))-3

f(\frac{\pi}{4})=-2\cos(\pi)-3

f(\frac{\pi}{4})=-2(-1)-3

f(\frac{\pi}{4})=2-3

f(\frac{\pi}{4})=-1

So now we need to compute the change in f over the change in x:

\frac{-1-(-5)}{\frac{\pi}{4}-0}

\frac{-1+5}{\frac{\pi}{4}}

Dividing by \frac{\pi}{4} is the same as multiplying by \frac{4}{\pi}:

(-1+5)\cdot \frac{4}{\pi}

4 \cdot \frac{4}{\pi}

\frac{16}{\pi}

gl648809
gl648809
4,4(45 marks)

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

d+d=14

2d=14

d=\dfrac{14}{2}

d=7

Therefore, the correct option is 1.

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