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barxatty [35]
3 years ago
8

A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h = − 1

6 t 2 + 116 t + 96 models the ball's height above the ground, h , in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

Mathematics
2 answers:
olga2289 [7]3 years ago
6 0

Answer:

  a) 306.25 ft

  b) 8 seconds

Step-by-step explanation:

a) The time at the maximum height is found from the equation for the axis of symmetry:

  ax^2 +bx +c   has axis of symmetry at x=-b/(2a)

For the given equation, the t-value at the vertex is ...

  t = -116/(2(-16)) = 3.625 . . . seconds

At that time, the height is ...

  h = (-16(3.625) +116)(3.625) +96 = (58)(3.625) +96 = 306.25

The maximum height is 306.25 feet.

__

b) The ball will hit the ground when h=0. From the vertex values in the first part, we know we can rewrite the equation in vertex form as ...

  h(t) = -16(t -3.625)^2 +306.25

This will be 0 when ...

  0 = -16(t -3.625)^2 +306.25

  (t -3.625)^2 = 306.25/16

  t = 3.625 +√19.140625 = 3.625 +4.375 = 8

The ball will hit the ground after 8 seconds.

Bas_tet [7]3 years ago
3 0

Answer:  a)  306.25 feet   b) 8 s

Step-by-step explanation:

Actually we have to find the function' s  h(t)  maximum meaning.

To do that we have to find the corresponding t - let call it t max

As known t max= (t1+t2)/2 where t1 and t2 are the roots of quadratic equation' s  

Lets find the roots t1 and t2

-16*t^2+116*t+96=0   divide by 4 each side of the equation

-4*t^2 +29*t+24=0

D=29^2+24*4*4=1225 =35^2

t1=(-29-35)/(-8)=8

t2=(-29+35)/(-8)=-6/8=-3/4=-0.75

t max=  (8+(-0.75))= 7,25/2=3.625 s

h max= -16*t max ^2+116*t +96= -16*3.625^2+116*3.625+96=306.25 feet

b) t2=8s is the time when the ball hits the ground.

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Answer:

The answer is 1.21.

Step-by-step explanation:

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I hope this was clear!

5 0
3 years ago
How do you find x for this question?
lilavasa [31]
X = 32.5 I believe..........
3 0
3 years ago
3% simple annual interest paid on $250
podryga [215]

Answer:

1st one is (0.03)(250)

2nd one is $7.50

3rd one is $30.00

Step-by-step explanation:

6 0
3 years ago
Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your con
Ket [755]

Answer:

Step-by-step explanation:

Given that:

H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55

(a) For x = 54 and s = 5.3

The test statistics can be computed as:

Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }

Z = \dfrac{-1}{\dfrac{5.3}{6} }

Z = -1.132

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-1.132,35,1) = 0.1326

Decision: p-value is greater than significance level; do not reject \mathbf{H_o}

Conclusion: \  There  \ is \  insufficient \  evidence  \  to \  conclude \  that \ \mu < 55

b

For x = 53 and s = 4.6

The test statistics can be computed as:

Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }

Z = \dfrac{-2}{\dfrac{4.6}{6} }

Z = -2.6087

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-2.6087,35,1) =0.0066

Decision: p-value is < significance level; we reject the null hypothesis.

Conclusion: \  There  \ is \  sufficient \  evidence  \  to \  conclude \  that \mu < 55

c)

For x = 56 and s = 5.0

The test statistics can be computed as:

Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }

Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }

Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }

Z = 1.2

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(1.2,35,1) = 0.88009

Decision: p-value is greater than significance level; do not reject \mathbf{H_o}

Conclusion: \  There  \ is \  insufficient \  evidence  \  to \  conclude \  that \ \mu < 55

6 0
3 years ago
A time/motion word problem
andriy [413]
The two planes are flying on the two legs of a right triangle.
The straight distance between them is the hypotenuse of the triangle.

Since the speeds are in mph, let's work the time in hours.
Call the time 'H' that we're looking for.
It's the number of hours after they both take off that they're 650 miles apart.

After 'H' hours, the first plane has gone 500H miles north.
After 'H' hours, the second plane has gone 1200H miles east.
After 'H' hours, they are 650 miles apart.

Do you remember this for a right triangle ? ==>    A² + B² = C²

(500H)² + (1200H)² = (650)²

250,000H² + 1,440,000H² = 422,500

1,690,000 H² = 422,500

H² = (422,500) / (1,690,000) = 0.25

H = √0.25 = 1/2 hour = 30 minutes
3 0
3 years ago
Read 2 more answers
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