Algebra help!!?

Question

I need someone to show me how they got the answer, I need to understand how to actually do the problem, not just copy the answer down plz!

A.) The perimeter of a rectangle is 29 feet. Express the area of the rectangle as a function of the length.

B.) A car purchased in 1999 was $35,000. Now has a bluebook value of $12,000 in 2006. Assuming that the depreciation in the value occurs at a constant rate, construct a function that will give the value of the car as a function of years since its purchase.

Also, how many yrs did it take for the car to depriciate to a value of $20,000?

And, What will the value of the car be in 2008?

Answer 1

2L + 2W = 29

A = LxW and 2W = 29-2L so W = (14.5-L)

so A = L x (14.5-L) or A =14.5L - L^2

second part:

$12,000 = $35,000 (f)^t where f is the depreciation and t=time

so 12000 = 35000 (f)^7 for 7 years

so 12000/35000 = (f)^7

so 0.3428 = (f)^7
so log 0.3428 = 7 log (f)
so -0.46488 = 7 log(f)
so -0.46488/7 = log (f)
so -0.0664 = log (f)
so (f) = .8582.
Now you have a formula for any period of time:
Value = 35000 (.8582)^t
in 2008 t=9
value = 35000 (.8582)^9 = $8838

Answer 2

For increasing cubic binomials the overall formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D