Mathematics, 16.07.2019 02:30 sciencefacts4504

Find the average rate of change of the function
f(x) = √x +1 on the interval 4 ≤ x ≤ 9. recall that
the coordinates for the start of the interval are (4,
3).
what are the coordinates for the end of the
interval?
o (9,4)
o (9,3)
o (9, 82)

Answers: 1

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Answers

Answer from: KariSupreme

A function describes the relationship between related variables.

The average rate of change of f(x) over 4 ≤ x ≤ 9 is $\frac 15$ .The coordinates of the end interval is (9,4)

Given that:

$f(x) = \sqrt x + 1,\ 4 \le x \le 9$

The average rate of change (m) is calculated as:

$m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

$m = \frac{f(9) - f(4)}{9 - 4}\\$

So, we have:

$m = \frac{f(9) - f(4)}{5}$

Calculate f(4)

$f(x) = \sqrt x + 1$

$f(4) = \sqrt 4 + 1$

f(4) = 2 + 1

f(4) = 3

Calculate f(9)

$f(x) = \sqrt x + 1$

$f(9) = \sqrt 9 + 1$

f(9) = 3 + 1

f(9) = 4

So, we have:

$m = \frac{f(9) - f(4)}{5}$

$m = \frac{4 - 3}{5}$

$m = \frac{1}{5}$

Recall that:

f(4) = 3 --- this represents the coordinate of the start interval

f(9) = 4 --- this represents the coordinate of the end interval

Hence, the coordinates of the end interval is (9,4)

Read more about average rates of change at:

link

Answer from: jtingley0502

Oops I went too far.

The other point is (9,4).

The average rate of change is 1/5.

Step-by-step explanation:

So I think your function is $f(x)=\sqrt{x}+1$ . Please correct me if I'm wrong.

You want to find the slope of the line going through your curve at the points (4,f(4)) and (9,f(9)).

All f(4) means is the y-coordinate that corresponds to x=4 and f(9) means the y-coordinate that corresponds to x=9.

So if $f(x)=\sqrt{x}+1$ , then

$f(4)=\sqrt{4}+1=2+1=3$ and

$f(9)=\sqrt{9}+1=3+1=4$ .

So your question now is find the slope of the line going through (4,3) and (9,4).

You can use the formula $\frac{y_2-y_1}{x_2-x_1}$ but I really like to just line up the points vertically and subtract then put 2nd difference over 1st difference. Like this:

( 9 , 4)

-( 4 , 3)

-------------

5 1

So the slope is 1/5.

The average rate of change of the function f on the interval [4,9] is 1/5.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$