# A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t² + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Answer: H(t) = -16t^2 +704t = -16(t^2 -44t)
Putting in vertex form: -16(t^2 -44t +484) + 704
h(t) = -16(t-22)^2 + 704
It takes 22 seconds to reach the maximum height, which is the vertex of the parabola at (22,704)

22 secs.

Step-by-step explanation:

h(t) = -16t^2 + 704t

The maximum will happen where the first derivative is equal to 0.

h’(t) = -32t + 704

-32t + 704 = 0 => -32t = -704 After subtracting 704 from both sides of the equation

Now divide both sides of the equation by -32

t = 22 secs.

Double Check: recalculated/reasonable ✅ ✅

Just an interesting aside. After 22 secs, the projectile will be -16(22)^2 + 704(22) = -7744 + 15,488 = 7744 units up as its maximum height.

## Related Questions

The surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=2 and h=4?

We know that
[surface area for a rectangular prism with a square base ]=2*s²+4*s*h

2*s²----> Is the surface area of the bases
4*s*h---> is the lateral area
s=2 units
h=4 units

[surface area for a rectangular prism with a square base ]=2*2²+4*2*4
surface area=8+32----> 40 units²

40 units²

40

Step-by-step explanation:

If the ratio of the radii of two spheres is 6 : 5, what is the ratio of the surface areas of the two spheres? 6 : 5

6r2ππ : 5r2ππ

36 : 25

216 : 125

Answer: Choice C) 36:25

To get this answer, we simply square each piece of the original ratio 6:5
6^2 = 36
5^2 = 25

Think of two squares where one has a side length of 6 and the other of 5. The ratio of the sides is 6:5. The areas of the two squares are 36 and 25 as mentioned above. So the ratio is 36:25. This idea can be applied to any surface area or area in general. It doesn't have to be two squares. The reason why we can apply this to any general shape is because we can break up the shape into small squares to get a rough approximation. The more squares we use, the better the approximation.

A 4-up number is defined as a positive integer that is divisible by neither 2 nor 3 and does not have 2 or 3 as any of its digits. How many numbers from 400 to 600, inclusive, are 4-up numbers? PLEASE ANSWER ASAP

There are 42 numbers

Explain how the value of the discriminant B^2-4AC can be used to predict the number of solutions an equation has? help me please

We need to know this:

If Δ > 0 we have two and different solutions

If Δ = 0 we just one solution

If Δ < 0 we don't have real solutions