Width: W
Length: L = W + 8
Perimeter = 2W + 2L = 2(W) + 2(W+8) = 184 (ft)
Solving for W: 2W + 2W + 16 = 184 (ft)
4W = 168 ft, and so W = 42 ft.
The length, L, is (42 + 8) ft = 50 ft. (answer)
Answer: 2^-10
Do you need an explanation?
The fastest way is to just use a scientific calculator.
To do it without a calculator, use prime factorization.
I'll only do the second one which is the answer.
27 x 8
= 3^3 x 2^3 = 6^3
Which is a perfect cube.
Answer:
(i) (f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = x³ + 4·x² + 5·x + 2
Step-by-step explanation:
The given functions are;
f(x) = x² + 3·x + 2
g(x) = x + 1
(i) (f - g)(x) = f(x) - g(x)
∴ (f - g)(x) = x² + 3·x + 2 - (x + 1) = x² + 3·x + 2 - x - 1 = x² + 2·x + 1
(f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = f(x) + g(x)
∴ (f + g)(x) = x² + 3·x + 2 + (x + 1) = x² + 3·x + 2 + x + 1 = x² + 4·x + 3
(f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = f(x) × g(x)
∴ (f·g)(x) = (x² + 3·x + 2) × (x + 1) = x³ + 3·x² + 2·x + x² + 3·x + 2 = x³ + 4·x² + 5·x + 2
(f·g)(x) = x³ + 4·x² + 5·x + 2
