$\text{Consider the function}\\
\\
h(t)=\cot(t) \text{ on the interval }\left [ \frac{\pi}{4}, \ \frac{3\pi}{4} \right ]\\
\\
\text{we know that the average rate of change of a funtion f(x) over the }\\
\text{interval [a, b] is given by}\\
\\
f_{avg}=\frac{f(b)-f(a)}{b-a}\\
\\
\text{so using this, the average rate of change of the given function is}$

$h_{avg}=\frac{h\left ( \frac{3\pi}{4} \right )-h\left ( \frac{\pi}{4} \right )}{\frac{3\pi}{4}-\frac{\pi}{4}}\\
\\
=\frac{\cot \left ( \frac{3\pi}{4} \right )-\cot \left ( \frac{\pi}{4} \right )}{\frac{3\pi-\pi}{4}}\\
\\
=\frac{(-1)-(1)}{\frac{2\pi}{4}}\\
\\
=\frac{-2}{\frac{\pi}{2}}\\
\\
\text{Average rate of change of function}=\frac{-4}{\pi}$

6 0

3 years ago

Translate the following and explain where these examples could be

ki77a [65]

A) x-6; you have x amount of money and pay 6 dollars for a hat.
b) 2(x2);

5 0

2 years ago

Two sides of a triangle are exactly the Same length. The length of the third side is four cm shorter than the two equal sides. F

liubo4ka [24]

Answer:

15 cm, 15 cm, 11 cm

Step-by-step explanation:

let the equal sides be x then the third side is x - 4

The perimeter is the sum of the 3 sides and is 41 cm , then

x + x + x - 4 = 41

3x - 4 = 41 ( add 4 to both sides )

3x = 45 ( divide both sides by 3 )

x = 15

x - 4 = 15 - 4 = 11

The sides are 15 cm, 15 cm, 11 cm

3 0

2 years ago