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Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles

Ugo [173]

By definition, the average rate of change is given by:

$AVR = \frac{f(x2)-f(x1)}{x2-x1}$

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

$f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2$

Evaluating for x = 3:

$f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18$

Then, the AVR is:

$AVR = \frac{18-(-2)}{3-(-2)}$

$AVR = \frac{18+2}{3+2}$

$AVR = \frac{20}{5}$

$AVR = 4$

For f (x) = 3x - 8:

Evaluating for x =4:

$f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4$

Evaluating for x = 5:

$f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7$

Then, the AVR is:

$AVR = \frac{7-4}{5-4}$

$AVR = \frac{3}{1}$

$AVR = 3$

For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

$f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15$

Evaluating for x = 4:

$f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8$

Then, the AVR is:

$AVR = \frac{8-15}{4-(-3)}$

$AVR = \frac{-7}{4+3}$

$AVR = \frac{-7}{7}$

$AVR = -1$

For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

$f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4$

Evaluating for x = 1:

$f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4$

Then, the AVR is:

$AVR = \frac{-4-(-4)}{1-(-1)}$

$AVR = \frac{-4+4}{1+1}$

$AVR = \frac{0}{2}$

$AVR = 0$

Answer:

from the greatest to the least value based on the average rate of change in the specified interval:

f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]

4 0

2 years ago

points P and Q lie 240 m apart in line with and on opposite sides of a communications tower. the angles of elevation to the top

Leona [35]

Answer:

The height of the tower is 130.5m

Step-by-step explanation:

In the question, we are given the following values:

The angles of elevation to the top of the tower from P = 50°

The angles of elevation to the top of the tower from Q = 45°

The angles of elevation to the top of the tower from P = 50°

Hence,cot P = 1/ tan(50°)

The angles of elevation to the top of the tower from Q = 45°

Hence, tan 45° = 1

In the question,we are told Points P and Q lie 240 m apart in line with and on opposite sides of a communications tower.

Therefore,

PQ = height of the tower( tan Q + 1/tan P)

240m = height of the tower( tan 45° + 1/ tan 50°)

240m = h(1 + 1/tan 50°)

h = (240 m)/(1 + 1/tan (50°))

h = 130.49863962 meters

Therefore, the height of the tower to the nearest tenth of a meter is 130.5 meters(m)

5 0

2 years ago

Please help I have no idea

marin [14]

The answer would be the top left one, and the correct answer would be 17/8 or 2 1/8.

4 0

2 years ago

In a survey, Damian found that 75% of the total number of teenagers surveyed like pop music. If 150 teenagers like pop music, wh

djyliett [7]

Answer:

200 teenagers

Step-by-step explanation:

150÷0.75= 200

checking work:

200•0.75= 150

hope this helps chu <3

7 0

2 years ago

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A local Latin restaurant specializes in Peruvian, Cuban, and Tex-Mex cuisines in their recipes. Lomo Saltado, “Beef Stir-fry,” i

Vikentia [17]

Answer:

The cost per meal not including the $5

Step-by-step explanation:

or whatever is says something like that

3 0

2 years ago

Read 2 more answers