Step-by-step explanation:
d(t) = -16t² + 96t + 112
A) The quarter's initial height is at t = 0.
d(0) = -16(0)² + 96(0) + 112
d(0) = 112
The quarter is tossed from a height of 112 feet.
B) The maximum height is at the vertex of the parabola, which is at x = -b/(2a).
t = -(96) / (2 × -16)
t = 3
The quarter reaches its maximum height after 3 seconds.
C) d(3) = -16(3)² + 96(3) + 112
d(3) = 256
The quarter reaches a maximum height of 256 feet.
D) When the quarter lands in the water, d(t) = 0.
0 = -16t² + 96t + 112
0 = t² − 6t − 7
0 = (t + 1) (t − 7)
t = -1 or 7
Since t can't be negative, t = 7. So the quarter lands in the water after 7 seconds.
Volume is length x width x height so 24 x 12 x 18 is your answer
The ratio 2 to 5 means there are 2 cats and 5 dogs but the 5 to 2 ratio means there are 5 cats and 2 dogs.
Answer:
x = 3 sqrt 2
Step-by-step explanation:
We know that this is a 45, 45m 90 special right triangle. In this special right triangle the side lengths are x, x and the hypotenuse is x sqrt 2 (we can prove this using pythagoreans theorem). 6 is the hypotenuse, meaning that it is equal to x sqrt 2:
6 = x sqrt 2
x = 6/sqrt 2
Rationalize the denominator:
x = (6 sqrt 2)/2
x = 3 sqrt 2
Answer:
f(x) x^3 - 2x^2 + 5x + 12
Step-by-step explanation:
Next time please share the goal. I'm guessing your intent was to multiply out the given function.
f(x) = (x^2 + x - 3x - 3)(x - 4), or
= (x^2 - 2x - 3)(x - 4)
Now apply the distributive property of multiplication:
f(x) = x^3 - 4x^2 - 2x^2 + 8x - 3x + 12, or
= x^3 - x^2(4 - 2) + x(5) + 12, or
f(x) x^3 - 2x^2 + 5x + 12
