Mathematics High School

30 Points! A soccer ball hit from the ground into the air and is modeled by the function
h(t)=-16t^2+48t+2 (see attachment)

30 Points! A Soccer Ball Hit From The Ground Into The Air And Is Modeled By The Function H(t)=-16t^2+48t+2

Answers

Answer 1

Answer:

A)

At t = 3/2

B)

36 feet

Step-by-step explanation:

The soccer ball is modeled by the function:

[tex]h(t)=-16t^2+48t[/tex]

Where h(t) represents the height in feet of the ball over time t.

Note that this is a quadratic equation.

Part A)

Since this is a quadratic, the maximum height will be reached when the ball reaches its vertex.

So, we will find the x-coordinate of the vertex.

The vertex is given by:

[tex]\displaystyle \Big (-\frac{b}{2a} , h( -\frac{b}{2a} ) \Big)[/tex]

In this case, a = -16 and b = 48. Thus, the t-coordinate is:

[tex]\displaystyle t=-\frac{48}{2(-16)}=-\frac{48}{-32}=\frac{3}{2}[/tex]

The ball will reach is maximum height at t = 3/2.

Part B)

To find the maximum height, we can simply substitute the value back into the function and evaluated. Therefore:

[tex]\displaystyle\begin{aligned} h(\frac{3}{2})&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)\\ \\ &=-36+72\\\\ &= 36 \end{aligned}[/tex]

The maximum height of the ball is 36 feet.

Related Questions

Determine the x- and y- intercepts for the graph defined by the given equation.
x = -9

Answers

Answer:

X intercept is -3/7

one card from a deck of cards is selected, it is replaced, and another card is chosen. what is the probability that the first card is a red card and the second card is a diamond card?​

Answers

Answer:

the probability of a red card is 1/2 of 50% chance. The chance of a diamond card is 1/4 or 25% chance

Step-by-step explanation:

Answer as a fraction = 1/8

Answer in decimal form = 0.125

Answer as a percentage = 12.5%

==========================================

Explanation:

The probability of choosing a red card is 1/2 since half of the cards are red (the other half are black).

This card is selected and then put back into the deck. This means that the second selection will deal with the same number of total cards.

Since we have four suits, and one of those suits is diamonds, this means the probability of choosing a diamond card is 1/4.

We then multiply the fractions to get (1/2)*(1/4) = (1*1)/(2*4) = 1/8

The probability of getting a red card first, then a diamond card second, is 1/8

Use your calculator to find that 1/8 = 0.125 which converts to the percent form 12.5%

Write the equation in Standard Form.
y+1 = - 4 (x+4)

Answers

y+4x+7 is the answer

Answer:

y = -4x - 17

Step-by-step explanation:

y + 1 = -4 (x + 4)

First, distribute the -4

y + 1 = -4x - 16

Then subtract 1 from both sides to make the equation y=

y = -4x - 17

This makes the equation standard form

A group of friends wants to go to the amusement park. They have no more than $235 to spend on parking and admission. Parking is $7, and tickets cost $28.50 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.

Answers

228/28.50= 8 that should be right!

The solution of the inequality for the number of people (p) who can go to the amusement park will be;

⇒ p < 8

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

They have no more than $235 to spend on parking and admission.

And, Parking is $7, and tickets cost $28.50 per person, including tax.

Now,

Let the number of people who can go to the amusement park = p

So, We can formulate;

⇒ 28.50p + 7 < 235

Solve for p as;

⇒ 28.50p < 235 - 7

⇒ 28.50p < 228

⇒ p < 228/28.50

⇒ p < 8

Thus, The solution of the inequality for the number of people (p) who can go to the amusement park is;

⇒ p < 8

Learn more about the inequality visit:

brainly.com/question/13777972

#SPJ5

Solving For x.
[tex]2x + 5 = 1[/tex]
Step By Step Explanation, Please.
​

Answers

x = 3 I added a picture hope this helps
Subtract the 5 to the other side of the equal sign giving you -4. Divide -4 by the 2 leaving you with x= -2

Mitzi has 79 coins she divides the coins equally among herself and her 3 brothers Mitzi will keep any coins left over how many coins does each person get

Answers

Answer:

19

Step-by-step explanation:

79÷4=19R3

       ≈ 19

What is the distance between the points (−8, 5) and (−8, −1)?

Answers

Answer:

6

Step-by-step explanation:

The owner of a flower shop sells18 roses for $90.00. What is the cost in dollars per rose?

Answers

each rose is $5 bc 90/18 is 5

Mr. Takaya can eat three slices of pizza in five minutes. If he continues to eat at the same rate, how long will it take him to eat the whole pizza, which has twelve slices?

Answers

Answer:

20 minutes

Step-by-step explanation:

3 slices=5 minutes

12slices=20 minutes

because 4x3 is 12, 4x5=20 minutes

Hope this helps! :)

If f(x) = x and g(x) = 2, what is (f•g)(x)?

Answers

Answer:

A

Step-by-step explanation:

(f*g)(x)=(2)*(x)=2x

A

a bicycle store costs $3600 per month to operate .The store pays an average $80 per bike . The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?

Answers

3400

Step-by-step explanation:

3600-120=3480,3480+80=3560

Charles purchases a car for $50,187 at 1.9% add-on rate for 6 years.

Answers

Answer:

good for him

Step-by-step explanation:

Evaluate each expression for the given value of the variable. 11 + r; r=7

Answers

Hey there!

The answer is [tex]18[/tex]

To solve this, you simply plug in [tex]r[/tex] to the expression!

[tex]11+r; r=7[/tex]

[tex]11+7[/tex]

[tex]18[/tex]

Have an amazing day!

If r=7 then 11+7=18.. BOOM

Pls help me this is timed

Answers

Answer:

3 to the powered of 7

Step-by-step explanation:

Answer:

3^7 (note that it's not 3*7)

Step-by-step explanation:

3 is multiplied by itself 7 times, so the answer is 3^7(or three to the seventh power in word form)

How many 1/3 yard are in 4 yards

Answers

Answer:

12

Step-by-step explanation:

Answer:

Thats confusing

Step-by-step explanation:

Hm I would prob say 2/3 or 4/3 I dont  know  i'm not smart

Can you do 11 12 and 13 please?​

Answers

Answer:

11.3x=33(vertically opposite angle)

x=33/3=11

12.117=4x-11(vertically opposite angle)

117+11=4x

x=128/4=32

13.4x-7+x+16=68(given)

5x=68+7-16

5x=59

x=59/5

Can someone Please help me with this ??

Answers

D.
y = 2/3x - 2
the easiest way to do this without doing actual math is to just graph it

If you buy a car at a gash station for $5.00, the cost per gallon is $3.10. If you have $40, write and solve a linear equation to find the number of gallons of gas you can afford

Answers

Answer:

Step-by-step explanation:

1) Why would somebody buy a car at a gas station? For $5?

2) You would have $35 to spand on gas. 10 gallons would cost $31. Add 2 more gallons for $6.20.

The total is 12 gallons of gas for $37.20

SOHCAHTOA can anyone help me with this

Answers

Root of ( 20^2 - 16^2 ) = 12

Help me please I need it

Answers

Answer:

2,400=22%

9300=25%

12000=28%

6300=25%

Step-by-step explanation:

After Kim drank some of the orange juice, there was 183 mL of orange juice left in the bottle. When Kim bought the bottle of orange juice, there was 250 mL of orange juice. What was the percent of change in volume of orange juice

Answers

Answer:

I think the change in volume is 26.8%

Step-by-step explanation:

I'm really sorry if I'm wrong

I'm sorry please help.
Solve the following system of equations.
x-3y=17
x+7y=-23
x=
y=

Answers

Answer:

-4y=40

y=-10

x-3(-10)=17

x-30=17

x=17+30

x=47

Step-by-step explanation:

Answer:

x= 5

y= -4

Step-by-step explanation:

x= 17+3y so you substitute what you got for x in so

17 +3y +7y = -23

10y=-40

y=-4 now you put -4 in for y in the first equation

x = 17 + (3 times -4)

x = 17 - 12

x=5

someone help me please.

Answers

Answer:

3

Step-by-step explan

1 x 4/2 + 1

4/2 + 1

4 divide by 2 is = 2

2+1 = 3

so the value of 1 x b/2 + 1 is = to 3

Answer:

3

Step-by-step explanation:

1 x 4=4

4/2= 2

2+1=3

Have a good day UwU

The blue pen is 12 cm long the red pen is 72 mm long what is the difference between the 2 pens?

Answers

Answer:

the difference between the 2 pens is 4.8 cm

Determine the domain of the graph shown.
A) [0, 8]
B) [0, 24]
C) [0, 20]
D) [0, 10]

Answers

The answer isssssssss A

It took Jamie 3/4 of an hour to complete 1/4 of a puzzle. How many hours will it take to complete a puzzle?

Answers

Answer:

It will take Jamie 3 hours to complete it

Step-by-step explanation:

3/4 * 4/1 = 12/4 = 3 hours

Answer:

3 hours

Step-by-step explanation:

3/4x4/1=12/4

12/4=3

Carmen paid $10.50 for a T-shirt at the mall. It was on sale for 30% off. What was the original price before the discount? *

Answers

Answer:

15

Step-by-step explanation:

70%-> 10.50

100%-> 15

how many significant figures does the value of 0.080 have?​

Answers

It has 2 sig figs in

Answer:

2 Significant figures

Step-by-step explanation:

The 8 is the first significant figure since all non zeros are significant.

The 0 after the 8 is also significant since it's a zero after the decimal point and an integer.

my school bag contains 9 books each mass 2/9 kg and 5 folder each mass 7/25 kg what is the total mass of books and folders in my bag​

Answers

9*2/9= 18/9= 2kg
5*7/25= 35/25= 1 10/25= 1 2/5 kg
1 2/5kg+2kg= 3 2/5kg or 3.4kg
total mass equals 3 and 2/5kg or 3.4kg

The mass of a package sent through the mail is 3 kilograms what is the mass of the package in grams? Plz halp GAHAAHAHHAH

Answers

Answer:

3000 grams

Step-by-step explanation:

convert 3 Kg to G

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