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andreev551 [17]
3 years ago
9

Vanessa throws a tennis ball in the air. The function h(t) = -15t2 + 45t + 10 represents the distance in feet, that the ball is

from the ground at any time in seconds, t. What is the maximum height of the ball?
Mathematics
1 answer:
Step2247 [10]3 years ago
5 0

Answer:

43.75feet

Step-by-step explanation:

Given the height of the tennis ball expressed as;

h(t) = -15t^2 + 45t + 10

At maximum height, the velocity of the ball is zero

v = dh/dt

dh/dt = -30t + 45

Since dh/dt = 0, hence;

0 = -30t + 45

30t = 45

t = 45/30

t = 3/2

t = 1.5secs

Substitute t = 1.5 into the expression given

h(1.5) = -15(1.5)^2 + 45(1.5) + 10

h(1.5) = -15(2.25)+67.5+10

h(1.5) = -33.75+77.5

h(1.5) = 43.75feet

Hence the maximum height of the ball is 43.75feet

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If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height
german

Answer:

Time = 7.5\ seconds

Step-by-step explanation:

Given

Equation:\ h(t) = -16t^2 + 120t

Initial\ Velocity = 160ft/s

Required:

Determine the time taken to return to the ground

From the equation given; height (h) is a function of time (t)

When the rocket returns to the ground level, h(t) = 0

Substitute 0 for h(t) in the given equation

h(t) = -16t^2 + 120t

becomes

0 = -16t^2 + 120t

Solve for t in the above equation

-16t^2 + 120t = 0

Factorize the above expression

-4t(4t - 30) = 0

Split the expression to 2

-4t = 0\ or\ 4t - 30 = 0

Solving the first expression

-4t = 0

Divide both sides by -4

\frac{-4t}{-4} = \frac{0}{-4}

t = \frac{0}{-4}

t =0

Solving the second expression

4t - 30 = 0

Add 30 to both sides

4t - 30+30 = 0+30

4t  = 30

Divide both sides by 4

\frac{4t}{4}  = \frac{30}{4}

t  = \frac{30}{4}

t = 7.5

Hence, the values of t are:

t =0 and t = 7.5

t =0 shows the time before the launching the rocket

while

t = 7.5 shows the time after the rocket returns to the floor

5 0
3 years ago
Which operation should be performed first according to the order of operations? 75 – 12 + 36 ÷ 3 + 14 • 8 A. 12 + 36 B. 75 – 12
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The one that should be performed according to the order of PEMDAS is 14 times 8.
P= PARENTHESIS 
E= EXPONENTS
M= MULTIPLICATION
D= DIVISION
A= ADDITION
S= SUBTRACTION
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3 years ago
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2 years ago
Maureen bought 200 shares of BETA Corp. for 12 1/2 per share. What was
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The purchase price of the stock includes the commission paid to the stockbroker. You have to multiply the cost per stock of the stock to the number of shares purchased by Maureen to get the purchase price. You have to multiply the purchase price with the percentage of commission to get the commission. You add the purchase price and the commission to get the total purchase price of the stock.

200 shares x $12.5 per share = $2,500

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4 0
3 years ago
How do you solve -5=4x-8
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Answer:

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Step-by-step explanation:

start with -5=4x+8

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divide each side by 4 to get your answer:

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