Answer:
Step-by-step explanation:
24) Since the area A of a rectangle is A = L * W, the length, L, is
A r³ - 24r - 5
------ = ------------------
W r - 5
Let's find the quotient (the length) using synthetic division:
5 / 1 0 -24 -5
5 25 5
--------------------------
1 5 1 0
Since the remainder is zero, we can take 1 5 1 as the coefficients of L, representing the length of the rectangle:
1x^2 + 5x + 1 = L
25) Recall that the area of a triangle of base B and height H is
A = (1/2)(B)(H). We need to calculate H from the given A and B.
Multiplying both sides of this equation by 2, we get 2A = (B)(H), or
2A 2(2c^3 + 16) 4(c^3 + 8)
(H) = ---------- = -------------------- = --------------- = 4(c^2 - 2c + 4) = (H)
B c + 2 c + 2
