Answer:
x = 27/8
Step-by-step explanation:
We can write a ratio to solve
x 3
------- = ----------
x+9 11
Using cross products
x*11 = 3(x+9)
11x = 3x+27
Subtract 3x from each side
8x = 27
8x/8 = 27/8
x = 27/8
Answer:
4, 3, -2 are the 3 roots of the function
SOLUTION:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is
S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to
obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45,
when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the
maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
I think the answer mightttttt beeeee hmmm
(3x+8)(3x+8)=
9x^2+24x+24x+64=
9x^2+48x+64
