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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

3 years ago

Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-

polet [3.4K]

Answer:

P(T) = 1/20 = 0.05

The probability of randomly selecting an umbrella and a shaving kit in that order is 0.05

Step-by-step explanation:

The probability of randomly selecting an umbrella and a shaving kit in that order.

P(T) = Probability of selecting umbrella first P(U) × probability of selecting shaving kit second P(S)

P(U) = 1/5 (1 umbrella out of five possible gifts)

P(S) = 1/4 (1 shaving kit out of four remaining possible gifts)

P(T) = 1/5 × 1/4

P(T) = 1/20 = 0.05

3 0

4 years ago

Hi guys can you answer my math question

dolphi86 [110]

Step-by-step explanation:

Put 1 on the far left and 4 on the far right.

Put. 2 the top and 3 at the bottom.

Put 5 in the centre.

There are 2 ways you can find to to make all the numbers add up to 5.

The number in the centre is the common anwser to the sums.

4 0

3 years ago

1/3ab^2 Solve for a

Julli [10]

Answer:

a = 18/b²

Step-by-step explanation:

Step 1: Write equation

1/3ab² = 6

Step 2: Solve for <em>a</em>

Multiply both sides by 3: ab² = 18
Divide both sides by b²: a = 18/b²

3 0

4 years ago

What is the weighted average cost of capital if a business has a cost of equity of 12%, a cost of debt of 10%, tax rate of 25%,

kvv77 [185]

If the cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity then the weighted average cost of capital is 10.875%

Given cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity.

We know that weighted average cost of capital= cost of equity* weight of equity+ cost of debt* weight of debt.

Cost of debt (consider after tax)=10%(1-25%)

=10%*0.75

=0.075

Weight of equity=60/80

=0.75

Weight of debt=20/80

=0.25

Weighted average cost of capital=12%*0.75+0.075*0.25

=0.09+0.01875

=0.10875

=10.875%

Hence the weighted average cost of capital is 10.875%

Learn more about weighted average at brainly.com/question/18554478

#SPJ4

8 0

2 years ago