Answer:
The boat will be approaching the dock at 12.05 ft. per min.
Step-by-step explanation:
See the attached diagram.
Let, P is the position of the pulley and B is the position of the boat.
So, from the right triangle Δ ABP,
AB² = PB² - AP² .............. (1)
= 90² - 8²
= 8036
⇒ AB = 89.64 ft.
Now, differentiating equation (1) with respect to time, t in minutes, we get
{Since AP is constant}
⇒
⇒ ft. per minute.
Therefore, the boat will be approaching the dock at 12.05 ft. per min. (Answer)
Answer: what does x =
Step-by-step explanation:
Answer:
y = - (x - 3)² + 15
Step-by-step explanation:
using the method of completing the square
y = x² + 6x + 6 ← factor out - 1 from the first 2 terms
y = - (x² - 6x) + 6
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
y = - (x² + 2(- 3)x + 9 - 9) + 6
= - (x - 3)² + 9 + 6
= - (x - 3)² + 15
Answer:natural number that you can not get by multiplying two natural numbers
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Given the definitions of f(x) and g(x) below,
f(x) = x^2+ x + 10
g(x) = -5x-3
f(g(x)) = f(-5x-3)
f(-5x-3) = (-5x-3)²+((-5x-3)+10
f(-5x-3) = 25x²+30x+9-5x-3+10
f(-5x-3) = 25x² +25x+16
f(g(x)) = 25x² +25x+16
f(g(-1)) = 25(-1)² +25(-1)+16
f(g(-1)) = 25-25 + 16
f(g(-1)) = 16
Hence f(g(-1)) is 16