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8090 [49]
3 years ago
6

A ball is thrown strait up from the top of a 64 foot tall building with an initial speed of 48 feet per second. The height of th

e ball as a function of time can be modeled by the function h(t)=-16t^2+48t+64. At what other time will the ball be at a height of 64 feet? How long will it take for f ball to reach its maximum height? What is he maximum height reached by the ball? How long willlit take for the ball to hit the ground?
Mathematics
1 answer:
Mrrafil [7]3 years ago
4 0

Answer:

see below

Step-by-step explanation:

h(t)=-16t^2+48t+64

Find when h(t) = 64

64 = -16t^2+48t+64

Subtract 64 from each side

0 =  -16t^2+48t

Factor

0 = -16t( t-3)

Using the zero product property

-16t =0    t-3 =0

t=0 and t=3

Other than at t=0,  so at t=3 seconds

How long will it take for f ball to reach its maximum height?

Find the vertex

t = -b/2a = -48 / ( 2 * -16) = -48/ -32 = 1.5 seconds

It will reach the maximum height at 1.5 seconds

What is the maximum height reached by the ball?

The height will be

h(1.5) = -16*(1.5)^2+48(1.5)+64

       = -36+72+64

       = 100

The maximum height is 100 ft

How long will it take for the ball to hit the ground?

h(t) =0

0=-16t^2+48t+64

Factor

0 = -16( t^2 - 3t -4)

0=- 16( t-4) (t+1)

Using the zero product property

t-4=0     t+1=0

t =4     t = -1

Since time cannot be negative

t=4 seconds

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kolbaska11 [484]

Answer:

22. Perimeter = 52 units

     Area = 160 Square Units

23. Notation form :  2 \times 10^{5}

     Standard Form : 200000

Step-by-step explanation:

22.

The formula for perimeter is

P = 2 (length + Width )

  = 2 ( 2x+3x+1)

  =  2(5x+1)

The Formula for Area of a rectangle is

A= length x width

A= 2x \times (3x+1)

A=6x^2+2x

Now we have to find the Perimeter and Area for x = 5

P = 2(5 x 5 +1)

P= 2(26)

P=52 units

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A= 150 + 10

A= 160 square units

23.

A. By using rule of exponents , we can determine that both the results will be same.

B.

Miriam's calculation

\frac{2.8 \times 10^{9}}{1.4 \times 10^{4}}

\frac{2.8}{1.4} \times 10^{9-4}

2 \times 10^5

Priya's calculation

\frac{2.8 \times 10^{2}}{1.4 \times 10^{-3}}

\frac{2.8}{1.4} \times 10^{2-(-3)}

2 \times 10^5

Standard notation

2 \times 10^5 = 200000

4 0
3 years ago
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