The inches of rainfall in the rainforest is represented by the function f(x) = 3(x-2)+ 4. What is the average rate of change between the 2nd year and the 6th year?

The average rate of change of rainfall in the rainforest between 2nd year and 6th year = 3 inches

Step-by-step explanation:

Given function representing inches of rainfall:

To find the average rate of change between the 2nd year and the 6th year.

Solution:

The average rate of change between interval is given as :

For the given function we need to find the average rate of change between 2nd year and 6th year.

So, we have:

Thus, average rate of change will be:

⇒

⇒

⇒

Thus, the average rate of change of rainfall in the rainforest between 2nd year and 6th year = 3 inches

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15