Atoy rocket is launched from a platform that is 48 ft high. the rocket height above the ground is modeled by h=-16t^2+32t+48. a) find the maximum height of the rocket b) find the time it will take for the rocket to reach the ground

a) 64 feet

b)  3 seconds

Step-by-step explanation:

a)

The maximum height of can be bound by finding the y-coordinate of the vertex of .

Compare this equation to to find the values of .

.

The x-coordinate of the vertex can be found by evaluating:

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating at :

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

I'm going to divide both sides by -16:

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

This implies we have either or

The first equation can be solved by adding 3 on both sides: .

The second equation can be solved by subtracting 1 on both sides: .

So when seconds, is when the rocket has hit the ground.

just keep asking questions until you have a better understanding.

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)