A) can be done using u-substitution .... Let u = x^2, du = 2x dx
C) can be done using trig identity ... cos(2x) = 1 - 2sin^2
B) can only be done using integration by parts. It is a product of 2 distinct functions and a u-sub does not simplify the integral.
Answer:
r=8
t=4√29
Step-by-step explanation:
By the altitude leg theorem:
This implies that:
We simplify to obtain:
By the Pythagoras theorem:
Answer:
Step-by-step explanation:
Let he speed of the boat on the lake is x.
<u>Considering the speed of the current it will take him:</u>
- 22.5/(x + 6) + 22.5/(x - 6) = 9
- 2.5 / (x + 6) + 2.5 / (x - 6) = 1
- 2.5(x - 6 + x + 6) = (x + 6)(x - 6)
- 2.5*2x = x² - 36
- x² - 5x - 36 = 0
- x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
- x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)
