The function f(x) = 582(7)x represents the growth of a mosquito population every year in a remote swamp. troy wants to manipulate the formula to an equivalent form that calculates every 2 months, not every year. which function is correct for troy's purposes?

The required function is,

Step-by-step explanation:

Since, the population which is increasing with the constant factor is,

Where, a is the initial population,

b is the growth factor per period,

x is the number of periods.

Here, the given function that represents the mosquito population after x years,

Where, 7 is the growth factor per year,

Since, 12 months = 1 year,

2 month = 1/6 year.

Also, we can write,

Which is the required equivalent function that shows the population of mosquito is increasing in every 2 month by the growth factor .

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

6^2 or 36

step-by-step explanation:

6000n

6×1000n

6×10^3 n

so we need 6n need to be a perfect cube

so n has to be 6^2 so that 6n is 6^3

what i'm saying is if you let n be 6^2 you have 6^3×10^3 or 60^3 which is a perfect cube