David kicks a ball off the ground. After t seconds, it’s height, h (in feet), is given by the formula h=-16t^2+80t. How many seconds does the ball reach its maximum height? What is the maximum height reached by the ball?

Answers

Answer 1

Answer:

The ball reaches its maximum height at 2.5 seconds

The maximum height is 100 feet

Step-by-step explanation:

Maximum Value of Functions

We use the derivative of a function to find its maximum or minimum value over a given interval.

Given a function y=f(x), the first derivative criterion establishes if x=a is such that:

f'(a)=0, and f''(a) < 0 then x=a is a maximum of f.

The height h in feet of a ball after t seconds is:

[tex]h(t)=-16t^2+80t[/tex]

Find the first derivative:

[tex]h'(t)=-32t+80[/tex]

Equate to 0:

[tex]-32t+80=0[/tex]

Subtract 80:

[tex]-32t=-80[/tex]

Divide by -32:

[tex]t = -80 / (-32) = 2.5[/tex]

t=2.5 seconds

Find the second derivative:

h''(t)=-32

Since h''(t) is always negative, then

The ball reaches its maximum height at 2.5 seconds

To find the value of the maximum height, substitute t=2.5 into the function:

[tex]h(2.5)=-16(2.5)^2+80*2.5=-100+200 = 100[/tex]

The maximum height is 100 feet


Related Questions

PLEASE HELP! Will give brailiest to the best answer!!!


What was a contributing factor to the growth of ranching during the Republic of Texas era?



F. the wild cattle left from Spanish herds

H. the increase in the number of slaves in Texas

G. the growth of railroads

J. the introduction of barbed wire

Answers

Answer:

H. the increase in the number of slaves in Texas

An album is 20cm long and 14 cm wide. Sal uses some lace to make an edge around the cover of the album. She has 12 cm of lace left over afterwards. How long was her piece of lace?

Answers

Her piece of lace was 80 cm.

2(14)+2(20)+12
28+40+12
=80


What is the third term of the sequence?
A
25
B
50
C. 35
D
20

Answers

Answer:

C

Step-by-step explanation:

35 is the third term of the sequence

Have a great day

Solve for b: 4b + 8/ -2 = 10

Answers

Answer:

The answer is b= 7/2

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

4b-4+4=10+4

4b=14

4b/4 =14/4

B=7/2

15 5/12 minus 11 1/8 A. 4 7/24 B. 4 7/12 C. -4 1/3 D.-4 7/24

Answers

Answer:

A. 4 7/24

Step-by-step explanation:

subtract 15 - 11 which equals 4

then do 5/15 - 1/8 =7/24

How to Rewrite 8 + 36 as a product of their GCF and the sum of two factors

Answers

Answer:

4 (2 + 9)

Step-by-step explanation:

  Given expression:

              8 + 36

The greatest common factor is the highest number that divides a number:

8 and 36 ;

  Factors of 8 : 1,2,4, 8

                  36 : 1, 2, 3, 4, 9, 18, 36

The highest common factor is 4;

  8 + 36  = 4 (2 + 9)

Matt runs in the park every day at the average rate of c meters per minute.

b:

If Matt runs triple his regular speed for 20 minutes, what distance would he cover?

Answers

Answer: 60c

Step-by-step explanation: 3c times 20. This is the right answer I hope it helps <3

Please help me solve for x

Answers

Answer:

x = 4

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, thus

7x - 4 = 24 ( add 4 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

c and e are expressions.

b is an equation.

a and d are inequalities.

Expressions are the only ones WITHOUT an 'equals', 'greater', or 'less than'.

( = , > ,. < )

Find the y-intercept of the following equation. Simplify your answer. y = 8x + 10 y-intercept=​

Answers

Answer:

10

Step-by-step explanation:

❗️Help needed please ❗️

Answers

Answer:

prove it by S.S.S axiom bro

Step-by-step explanation:

statement                                reason

1.in triangle ADB and ADC

a. AB=AC                                    a.given

b.BD=CD                                     b. radii of same circle

c. AD=AD                                      c. common side

2. ∵triangle ADB is congurent to 2. by S.S.S axiom

  ADC

Answer:

AD cuts BC at I => I is the midpoint of BC => BI = CI

ΔAIB and ΔAIC have:

AB = AC

BI = CI

m∠ABC = m∠ACB ( because ΔABC is a  isosceles triangle)

=> ΔAIB ≅ ΔAIC (sas)

=> m∠BAD = m∠CAD

ΔADB and ΔADC have:

m∠BAD = m∠CAD

AB = AC

AD is the common edge

=> ΔADB ≅ ΔADC (sas)

Step-by-step explanation:

I need you guys to answer all of this sorry please help me before 11:59 I beg

m<1

m<2

m<3

m<5

m<6

m<7

m<8

Here are the choices you have for each one (choose one)
106

74

74

Answers

Answer:

M<1 = 106

M<2 = 74

M<3 = 106

M<4 = 74

M<5 = 106

M<6 = 74

M<7 = 106

M<8 = 74

Step-by-step explanation:

what goes into 125 3 times

Answers

Answer:

41r6

Step-by-step explanation:

you dived 125 by 3

Answer:

Loading Answer...

Step-by-step explanation:

Loading Explanation...

what is 111 × 111 ÷ 14 ​

Answers

880.0714285714286 on my calculator

But I guess it rounds to 880.7 or 881

Answer:

880.071428571

Step-by-step explanation:

You could use a calculator btw but its ok happy to help :D

3t+3/5 =6 solve for t

Answers

Answer:

t=9/5

Step-by-step explanation:

PLEASE HELP NEED ASAP

Answers

What the formula?
::::::::::::::::::::::::::::::1

How many times does 2/3 go into 7 1/3

Answers

Answer:

11

Step-by-step explanation:

7 1/3 ÷ 2/3 = 11

(please give brainliest)

Answer: 1/11

Explanation:

KCF

(keep, change, flip)

Nadia is a stockbroker. earns ​13% commission each week. Last​ week, sold ​$7,000 worth of stocks. How much did make last week in​ commission? If averages that same amount each​ week, how much did make in commission in​ 2011?

Answers

Answer:

a). Nadia made a total of $825 last week in commission sales

b). The total amount Nadia in commission in 2011=$42,900

Step-by-step explanation: Step 1

Express the amount in commission she earns from her sales as follows;

C=S×r

where;

C=commission earned

S=total value of stock sales

r=commission rate

In our case;

C=unknown

S=$7,500

r=11%=11/100=0.11

replacing;

C=11% of 7,500

C=(11/100)×7,500

C=0.11×7,500=825

Nadia made a total of $825 last week in commission sales

b). To express the total amount she made in 2011, we derive the formula below;

Total amount (2011)=Average weekly commission×number of weeks in 2011

where;

Average weekly commission=$825

number of weeks in 2011=52

replacing;

Total amount (2011)=(825×52)=42,900

The total amount Nadia in commission in 2011=$42,900

Answer:

jjhjjh

Step-by-step explanation:

nn

the temperature in an experiment is increased at a constant rate over a period of time until the temperature reaches 0 degrees celsius. the equation y=5/2x-70 gives the temperature y in degrees celsius x hours after the experiment begins. Find and interpret the x- and y- intercepts.

Answers

Answer:

x = 28 (So it takes 28 hours for the temperature to reach 0°C.)

y = -70 (So the temperature when the experiment begins is −70°C.)

Step-by-step explanation:

To find the the x value, you remove the y value or replace it with 0.

0 = 5/2x - 70

Next you move the variable.

70 (2/5) = x           (multiply 70 by 2 to get 140 and divide that by 5)

And now you simplify to get:

28

To find the y value, you remove the x value or replace it with 0.

y =  0 - 70

And now you simplify to get:

-70

x = 28

y = -70

x = 28 (So it takes 28 hours for the temperature to reach 0°C.)

y = -70 (So the temperature when the experiment begins is −70°C.)

Is it (sometimes true/never true) that all three altitudes of a triangle fall outside the triangle?

Answers

never true is always 180

A stovetop burner on medium reaches 95°C. Which will also receive a flow of heat directly from the burner

Answers

Answer:

The surrounding air

Step-by-step explanation:

Answer:

the surrounding air

Step-by-step explanation:

Find the equation of a line through the coordinate (3,−2) and parallel to the line represented by y=12x−2.

Answers

Answer:

Step-by-step explanation:

y + 2 = 12(x - 3)

y + 2 = 12x - 36

y =12x - 38

The required equation of the line passing through (3, -2) and parallel to the line represented by y = 12x - 2 is y = 12x - 38.

What is Slope?

Slope is usually denoted by m.

Slope is defined as the change in the value of the y coordinates with respect to the change in the value of x coordinates.

Equation of a line in slope intercept form is y = mx + c where m is the slope and c is the y-intercept.

y-intercept is the y coordinate when x coordinate equals zero.

It is given that the required line is parallel to y = 12x - 2.

Comparing with the slope intercept form of the line, the slope of  y = 12x - 2 is 12.

Slope of two parallel lines are equal.

So the slope of the required line = 12

It is also given that required line passes through the point (x, y) = (3, -2).

Substituting these values,

-2 = (12 × 3) + c

-2 = 36 + c

c = -2 - 36

c = -38

So the required equation is found by substituting m = 12 and c = -38.

y = 12x - 38

Hence the equation of the line passing through (3, -2) and parallel to the line y = 12x - 2 is y = 12x - 38.

To learn more on Slope, click:

https://brainly.com/question/3605446

#SPJ2

Please help! What is the slope of the line graphed on the coordinate plane?

Answers

Answer:

The slope is 3/4

Step-by-step explanation:

You can Y2-Y1/X2-X1 to find the answer to this question

Since the points are (-2,3) and (2,6) it will be..

6-3/2+2   ** the 2 becomes a plus in the denominator because negative and negative is positive

3/4 is the slope

HELP ASAP. ‼️‼️‼️‼️‼️

Answers

Answer:

Nice Shoes..

Step-by-step explanation:

The answer is 16 to the 4th power for #1     89c for #2         and 29f for the third

How many grams are equivalent to 75 kilograms?

Answers

Answer:

75 * 1000 = 75000

75000 gram

Step-by-step explanation:

1 kg = 1000g, so the answer is simple (kg * 1000 = g)

PLEASE HELP 4. The Buff City Soaps in Arlington is counting how many soaps and bath bombs they sell in a given day. In total, they sold 33 bath products. The number of soaps they sold was one more than three times the number of bath bombs. WRITE THE SYSTEM OF EQUATIONS.​

Answers

Answer:

33 = x + (3x + 1)

x = bath bombs

So 3x is three times as many bath bombs, then the plus one makes it so that the soaps sold is more than three times the amount of bath bombs sold

The total operating cost to run the organic strawberry farm varies directly with its number of acres. What is the constant of variation in this scenario?

Answers

Answer: 16 acres

Step-by-step explanation: we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the number of acres

y ---> total operating costs

we have the ordered pair (20,551,520)

For x=20 acres, y=$551,520

Find the value of the constant of proportionality k

substitute the values of x and y

The linear equation is equal to

Find out how many acres are on a farm with a total operating cost of $441,216

so

For y=$441,216

substitute in the linear equation the value of y and solve for x

the answer is 16 acres

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

x ----> the number of acres

y ---> total operating costs

we have the ordered pair (20,551,520)

For x=20 acres, y=$551,520

Find the value of the constant of proportionality k

substitute the values of x and y

The linear equation is equal to

Find out how many acres are on a farm with a total operating cost of $441,216

so

For y=$441,216

substitute in the linear equation the value of y and solve for x

Step-by-step explanation:

How many more times larger is 8,000 than 8?

Answers

Answer:

8,000 is 1,000 times bigger than 8

Answer:

1,000 times bigger because you have to add the 0's in it.

Step-by-step explanation:

What is de DOMAIN of {(-2, 6) (4 , 9) (5, 12)} *
{6,9,12)
{-2,4,5)
6 sy s 12
-25x55

Answers

{-2,4,5). The second one.

) If a deposit or withdrawal will change an account balance by more
than $1,000, a manager must approve it. Which of these deposits and
withdrawals need manager approval? Choose ALL the correct answers.
-$875
-$1,600
$1,304
-$2,505
$1,001
$451
DONE
ID

Answers

The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

What are the deposits and withdrawals?

A deposit is a money put into a bank account for safekeeping until you need it. A withdrawal is a money that's taken out of your account.

The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

The deposits and withdrawals that do not require manager approval are:

-$875 (since it changes the balance by less than $1,000)

$1,304 (since it changes the balance by less than $1,000)

$1,001 (since it changes the balance by less than $1,000)

$451 (since it changes the balance by less than $1,000)

Therefore, The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

To learn more about deposits and withdrawals visit,

https://brainly.com/question/25920201

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