Algebra 2 question.?

Question

Suppose a baseball is shot up from the ground straight up with an initial velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
•16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
•v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
•s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.


What is the maximum height of the ball? What time will the maximum height be attained?

""""64 feet per second"""
1 sec= 64 feet.

Answer 1

s = -16t^2 + 64t + 0 (see other problem for setup)
The maximum of a parabolic function is obtained halfway between start and finish. You know from your other question that t = 4 when the ball hits the ground, so the maximum will occur halfway between 0 and 4, at 2.
s(2) = -16(2^2) + 64(2) = 64

64 feet after 2 seconds



Just for fun, I'll show you how to do this with calculus. You take the derivative of s, which is when you multiply the exponent by the coefficient and subtract one from the exponent:
s = -16t^2 + 64t
derivative of s = -16(2)t^(2-1) + 64(1)t^(1-1)
= -32t^1 + 64t^0
= -32t + 64
This is the equation for the velocity of the baseball, not the height. The maximum or minimum will be when the velocity is 0 because the ball stops moving up at its peak and starts moving down, so
-32t + 64 = 0
32t = 64
t=2

You don't need to know that but I thought I'd show you where we get our maximum. You'd only use that method if the ball weren't moving in a parabola.

Answer 2

you have s = -16t² + 64t + 0. at ground level, s = 0, so

-16t² + 64t = 0
t² - 4t = 0
t(t - 4) = 0
t = 0 .... on the ground at the start
t = 4 .... back to the ground 4 seconds later.

max height happens halfway between the zeros of the quadratic, at t = 2. when t = 2, s = -16(4) + 2(64) = 64 ft.

Answer 3

For increasing cubic binomials the final formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 4

87 feet, after 23 hours.

Tehe