A ball is thrown into the air. Its height (in feet) t seconds later is given by h(t)=64t−16t^2 a) What is the height of the ball 1 second after it has been thrown? b) After how many seconds does the ball hit the ground? c) At what time(s) is the ball 30 feet above the ground?

Answers

Answer 1

Answer:

A) 48 feet

B) 4 seconds

C) 0.54 seconds and 3.46 seconds

Step-by-step explanation:

So we have the function:

[tex]h(t)=64t-16t^2[/tex]

Which represents the height h(t) of the ball after t seconds.

A)

To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:

[tex]h(1)=64(1)-16(1)^2[/tex]

Simplify:

[tex]h(1)=64-16[/tex]

Subtract:

[tex]h(1)=48[/tex]

So, after 1 second, the height of the ball is 48 feet above the ground.

B)

To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:

[tex]0=64t-16t^2[/tex]

Solve for t. Factor out a 16t:

[tex]0=16t(4-t)[/tex]

Zero Product Property:

[tex]16t=0\text{ or } 4-t=0[/tex]

Solve for t:

[tex]t=0\text{ or } t=4[/tex]

We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.

C)

To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:

[tex]30=64t-16t^2[/tex]

First, divide everything by 2 to simplify things:

[tex]15=32t-8t^2[/tex]

Subtract 15 from both sides:

[tex]-8t^2+32t-15=0[/tex]

Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute:

[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]

Simplify:

[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]

Use a calculator. Approximate:

[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]

So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.

And we're done :)


Related Questions

The reduce feature on a copy machine is set at 84%. The picture being copied is 4.5 inches wide. What will be the width of yhe reduced picture?

Answers

Answer:

The answer is 3.825 inches, the reduced picture will be 84% of the size of the original

Answer:

3.78 inches

Step-by-step explanation:

if the original length is 4.5 and we are making it 84 percent of that size we multiply 4.5 times 84 percent(that is 0.84).

If we type in 4.5 * 0.84 on a calculator the answer comes back as 3.78

so the answer is 3.78 inches

Here is a polygon on a grid. An L shaped figure on a square grid. Draw a scaled copy of this polygon that has a perimeter of 30 units. What is the scale factor? Explain how you know.

Answers

Answer: the perimeter of this L shaped figure is 10 units, so scaling it by 3× would make the perimeter 30 units. so the scale factor is 3

The scale factor of the figure is 3 units.

We need to draw a scaled copy of this polygon that has a perimeter of 30 units and also we need to find the scale factor.

What is the scale factor?

The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.

If the sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor.

Now, scale factor = Scaled perimeter/Actual perimeter

From the figure, the perimeter of the figure is 10 units.

So, scale factor = 30/10 =3 units

Therefore, the scale factor of the figure is 3 units.

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Please help me with my homework :(

Answers

13. -5/6

14. -7/8

15 -7/10

Step-by-step explanation:

Plz help would the answer be -30

Answers

Answer:

Yes

Step-by-step explanation:

-27+(-3) can be simplified to -27-3

-27-3= -30

Answer: Yes you are correct. The answer is -30

Explanation:

We are adding 2 negatives. So we effectively add the positive versions of each number, and then make the result negative.

You can think of it in terms of money: you start off 27 dollars in debt and then borrow 3 more dollars to be a total of 27+3 = 30 dollars in debt.

Or you can think of it like you're under the ocean. Writing -27 could mean you're 27 feet below sea level. Adding on -3, ie subtracting 3, would then move you down 3 feet to get to 27+3 = 30 feet below sea level.

The information below represents the costs of Maggy’s home ownership. what does Maggy spend on average per month related to her home? Mortgage $1,309 per month

Answers

$2,152.58.

You can add the per month straight up, but you have to divide the annual costs by 12 (12 months in a year). Add all the numbers together, and you get (roughly) 2,152.58.

[tex]0.05x^{2}[/tex]how do i evaluate 0.05

Answers

You divide 0.05 by two

What type of number is pie/2 ?

Answers

Answer:

its a irrational number

What is the solution to this equation?
5x + 9 - 3x = 18 + 15
A. x= 3
B. x = 8
C. x = 12
D. x = 21​

Answers

Answer:

21

Step-by-step explanation:

5x-3x=18+15-9

2x=42 /:2

x=21

Add 15,7,.5 step by step please I'll mark u brainlest PLEASE

Answers

Answer:

27

Step-by-step explanation:

15+5=20

20+7=27

Answer: 27

Step-by-step explanation:

15+5=20

20+7=27

Name: Graphing in the Coordinate Plane
PLS I NEED YOUR HELP​

Answers

Basically all you have to do is go over (left from the center 5 spots) to -5 and up 3. You do x before y always. Then you put a p there because that is point p. I hope this helps you

Identify the property of equality that makes Equation 1 and Equation 2 equivalent.
Equation 1
4.2x – 1.5 = 1.7x + 8.3
Equation 2
42x - 15 = 17x + 83

Answers

multiplicative property if equality. explanation: you’re just multiplying by 10.

We use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.

Given,

Equation 1 - 4.2x – 1.5 = 1.7x + 8.3

Equation 2 - 42x - 15 = 17x + 83

We have to Identify the property of equality that makes Equation 1 and Equation 2 equivalent.

We have,

Equation 1 - 4.2x – 1.5 = 1.7x + 8.3

Equation 2 - 42x - 15 = 17x + 83

If we multiply 10 on both sides of the equation, we get

10 (4.2x – 1.5)  = 10 (1.7x + 8.3)

10 x 4.2x - 10 x 1.5 = 10 x 1.7x + 10 x 8.3

42x - 15 = 17x + 8.3

We get,

42x - 15 = 17x + 8.3 which is equivalent to equation 2.

This property is called the multiplicative property of equality.

Thus we use the multiplicative property of equality to make Equation 1 and Equation 2 equivalent.

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The graph shows the speed of a ball in free fall for 10 seconds. Which is the constant of proportionality shown in the graph? It's on TTM.

Answers

Answer:A

Step-by-step explanation:

c.
A train is traveling 1 mile every 75 seconds. If the train continues at this rate, then how
far will it travel in two hours?

Answers

Answer:

96 miles.

Step-by-step explanation:

2 hours = 2*60*60 = 7200 seconds.

So the required distance = 7200/75

= 96 miles.

Answer:

96 miles

Step-by-step explanation:

i did this a few months ago (coincidence I think not)

People drive, on average, 11,979 miles per year. About how many miles each week is that?
(Type a whole number or decimal rounded to the nearest tenth as needed)

Answers

Answer:

230.4

Step-by-step explanation:

11,979 divided by 52 is 230.365384615.

230.365384615 Rounded gets the answer

A scientist creates a colony of bacteria in a dish. This type of
bacteria duplicates itself per minute.
If at 9am the experiment started with a single cell and at 9:13
the dish was half-full, at what time will the dish be full?

Answers

Answer: 9:14

Step-by-step explanation: So if he started if 1 bacteria, it becomes 2 bacteria at 9:01, etc. So at 9:13, it is 2^13 and if that is half, that means 2^14 is when it is full so 9:14.

The dish will be full at  9:14 am.

Given, the bacteria duplicates itself per minute.

The experiment started with a single cell at 9 am and at 9:13 am the dish was half full.

So it is clear that after 13 minutes of experiment started the dish was half full.

Now, let here is only 1 bacteria in the dish which is duplicating per minute,so after 1 minute it becomes 2 after that it becomes 4 and after that it becomes 8. Hence it is clear from the example the bacteria doubles itself in powers of her minute. ([tex]2^x[/tex])  here x is the number of minute.

Since after 13 minutes the dish was half full, it means there are [tex]2^{13}[/tex] bacteria in the dish. hence the full dish is [tex]2^{14}[/tex] bacteria. so the bacteria will take 1 more minute for the dish to be full.

Hence at 9:14 am the dish was full.

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Find the inverse of the function: f ( x ) = 1 5 x + 4 Group of answer choices f − 1 ( x ) = 4 x − 5 f − 1 ( x ) = − 5 x − 4 f − 1 ( x ) = x − 4

Answers

Answer:

D

Step-by-step explanation:

So we have the function:

[tex]f(x)=\frac{1}{5}x+4[/tex]

To find the inverse, simply switch x and f(x), change f(x) to f⁻¹(x), and solve for it. Thus:

[tex]x=\frac{1}{5}f^{-1}(x)+4[/tex]

Subtract 4 from both sides:

[tex]x-4=\frac{1}{5}f^{-1}(x)[/tex]

Multiply both sides by 5:

[tex]f^{-1}(x)=5x-20[/tex]

So that's our inverse :)

So, our answer is D

Answer:

D

Step-by-step explanation:

A refrigerator sells for $1201. If the sales tax rate is 6.8%, what is the total price that you would pay for the fridge?

Answers

The answer is $1282.66

Explanation:

The sales tax rate (in this case 6.8%) is paid as part of selling a product. Also, to find the final price of a product, find the tax rate (percentage) of the price of the product and add this number to the price. The process to know the final price of the fridge is shown below:

1. Determine the 6.8% of $1201

 1.1. Write the values

1201  = 100  

 x     =  6.8

 1.2. Cross multiply and solve the equation

x100 = 8166

x= 8166 ÷ 100

x = 81.66

2. Add this value to the original price

$1201 + $ 81.66 = $1282.66 (Total price including the sales tax)

The last one Please answer asap im still crying

Answers

Answer:

He has 12 ten dollar bills

Step-by-step explanation:

Let t = number of 10 dollar bills

f = number of fifty dollar bills

t+f = 25  since he has 25 bills

solving for f

f = 25 -t

Then we know he has 770 dollars

10t+50f = 770

Using f = 25-t in the above equation

10t + 50 ( 25-t) = 770

Distribute

10t+ 1250 - 50t = 770

Combine like terms

-40t+1250 = 770

subtract 1250 from each side

-40t - 1250-1250 = 770-1250

-40t = -480

divide each side by -40

-40t/-40 = -480/-40

t =12

He has 12 ten dollar bills

CAN SOMEONE PLEASE HELP ME ASAP PLEASEEEE!!!​

Answers

Answer: being similar means they are in the same ratio. so x = 12

Step-by-step explanation:

first put it into a ratio, 4/x =2/6 and answer it like an equation.

4/x=2/6 (cross multiply)

24=2x

x=12

Answer:

x = 12

Step-by-step explanation:

The only full "pair" of sides is 2 on the little polygon and 6 on the big polygon. The relationship between them is 3. 2 × 3 = 6

Now, apply this to the pair we are using: 4 × 3 = x

4 × 3 = 12, so x equals 12.

[easy points] what is the verbal expression to this equation

Answers

Answer:

b

Step-by-step explanation:

BECAUSE x-25 = 3

shows something mines 25 that equals 3

What number divided by 9 is greater than 700?

Answers

Answer:

Any number greater than 6,300

Step-by-step explanation:

PLZZZZZZZZZZZ HELP!!!!!!!!!!!!!!!!

Answers

Answer:

A. Graph B

Step-by-step explanation:

The reasoning is because the 2 lines are parallel; therefore, it is impossible for them to overlap or intersect, which is the only way a solution can be found. Parallel lines can never have a solution. Hope this helped!

Should be graph b as the answer

The difference between a number x and 17 is 22

Answers

Answer:

X-17=22

X=22+17

X=39 this is the answer

the positive square root of 28?

Answers

Answer:

is 4 i think

Step-by-step explanation:

Please help :) which angles are supplementary

Answers

Answer:

The first one BED and DEA. AEC and BEC.

Step-by-step explanation:

Supplementary angles are 2 angles that when added equals 180. Also, if there are no numbers given, the 2 angles should make a straight line when next to each other.

Jack picks 5 pounds of apples in 8 minutes. Jill picks 6 pounds of apples in 10 minutes. Working together at these rates, how many pounds of apples will they pick in 40 minutes?

Answers

jill will pick up 24 and jack will pick up 25

Help please Thanks homework help

Answers

Answer:

30

Step-by-step explanation:

3x+x=4x

40+20=60

180-60=120

120/4=30

simplify the expression

Answers

Answer:

[tex]\sqrt[3]{215}[/tex]

Decimal Form: 5.99072641

Look down for explanation

Step-by-step explanation:

[tex]\sqrt[3]{215}[/tex]

You have to simplify.

[tex]= \sqrt[3]{215}[/tex].

Decimal Form: 5.99072641

Now you have the answer to your question!

Hope this helps!

Evaluate the expression if x = 3, y = 4 and z = 5. 6y - 2xy​

Answers

Answer:

the answer is 0

Step-by-step explanation:

6 (4) -2 (3)(4)

24-24=0

A chemist has 42 grams of aluminum. There are for aluminum. How many milliliters of aluminum does the chemist have?

Answers

Answer:

4,200 g. of aluminum

Step-by-step explanation:

42x100=4,200

The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum

How to determine the amount of aluminum?

The mass is given as:

Mass = 42 grams

The density of aluminum is:

Density = 2.7 g/cm³

So, we have:

Volume = Density/Mass

This gives

Volume = 2.7/42

Evaluate

Volume = 0.06429cm³

Convert to ml

Volume = 0.06429ml

Hence, the chemist has 0.06429ml of aluminum

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