On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet

Answer: The maximum height is 144 feet.

The maximum height is the y-coordinate of the vertex.  To find the vertex, we first use x = -b/2a.  For our information, that is x=-64/2(-16) = -64/-32 = 2.

Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144

they are right.

Step-by-step explanation:

things get better

Related Questions

9 11/12- 2 8/11 is a problem that i need help on

Hey there!!

Okay here are the steps you can follow!

9 11/12  ---->  improper fraction  ----> 119/12
2 8/11  ---->  improper fraction  ---->  30/11

119/12  -  30/11
(119/12  -  30/11) * 132
11(119)  -  12(30)
1309 - 360
949

Find the ratio of 3 3/4 to 7 1/4

15 : 29

Step-by-step explanation:

(3 3/4) / (7 1/4) = ((3·4+3)/4) / ((7·4+1)/4)

= (15/4) / (29/4) = 15/29

The ratio of the two numbers is 15 : 29.

What is 30/100 in simplest form

Step-by-step explanation: You can elimate a zero on each side, making 3/10

3/10

Step-by-step explanation:

1. 30/100 - Find the GCD

2. In this case the GCD is 10 since you can divide 30÷10 and 100÷10

3. 30÷10 = 3 and 100÷10 = 10

4. So it would be 3/10

So the final answer is 3/10

The sum of two numbers is 61 . The larger number is 5 more than the smaller number. What are the numbers?

35.5 and 25.5

Step-by-step explanation:

all you have to do is take 61÷2=30.5 and you add five to one of the halves, and subtract five form the other.

61÷2= 30.5

30.5+5= 35.5

30.5-5= 25.5

Kirk bought songs for his MP3 player. He needed 6 more songs to have a total of 100. Write an integer to represent how many more songs Kirk needs. I NEED HELP!!!!!!!

This is very easy to solve once you understanding writing equations. In this case, we could do n+6=100 because we know that the number of songs he has now (n) plus 6 will equal 100. Below is a solution for this equation.

n+6=100
-6     -6
n=94

After solving our equation, we know that Kirk has 94 songs.

A round cake has a diameter of 30 cm. Angela places the cake on a circular cake board with a diameter 5 cm longer than that of the cake. What is the circumference of the cake board? Give your answer in terms of pi π

C = 35 pi

Step-by-step explanation:

The new diameter is 5 + 30 = 35

The circumference = pi * d

The circumference = 35*pi

35π cm

Step-by-step explanation:

Hope this helps!

The Great pyramid of Giza has a square base with side length 755 ft. and original height of 481 ft. Determine its surface area. The answer is 923,285 ft. But i don't know how to get that answer. Please help.

The surface of pyramid is calculated by summing surface of its base and surface of its mantle.

Surface of base is easy to calculate. You have a square and its side is known therefore surface is:
Sb = a^2
Surface of mantle is a bit more complicated to calculate. First you have 4 sides of pyramid and each side is a triangle. To calculate surface of each triangle we need to know its height.
First we calculate side of triangle using Pitagorah's theorem.
s = √((d/2)^2 + H^2)   where d is diagonal of base which is square.
d = √2*a

Now again we have to use Pitagorah's theorem to calculate height of the triangle.
h = √(s^2 - (a/2)^2)

Now the surface of the triangle is calculated with:
St = (a*h)/2 and surface of mentle is:
Sm = 4*St.

Total surface of pyramid is:
Sb + Sm

What is an x and y intercept for 14x+y=140