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

what is the value of this?

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Answer:

4

Step-by-step explanation:

I used desmos

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1) A ratio of 2 to 10 is the same as
*
02/14
2/12
O 1/5
2/5

Answers

Answer:1/5

Step-by-step explanation:

Two and ten divided by two equals 1 and 5 so 1/5

please help thank you​

Answers

Answer:

B

Step-by-step explanation:

A=4 so its wrong cause the original one is 10-12=-2

what is true about the slopes of perpendicular lines

Answers

Slopes of parallel lines are equal.

help T^T ion wanna fail this class

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‘ you subtract 103-3=100 , then divide 100/10 =10 .. 10 is your answer

Plssss help what is the value of c

Answers

Answer:

5

Step-by-step explanation: The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

What is the sales tax on a $14,500 truck if the tax rate is 9%. What is the total price of the truck
after the sale tax?

Answers

Answer:

15805

Step-by-step explanation:

14,500×9÷100=1,305

14,500+1,305=15,805

I beg anybody please

Answers

Answer:

if no one answers pic b cuz i got good luck

Step-by-step explanation:

SOMEONE HELP IM STRESSING OUT

Answers

Answer: right angles x equals 7 and both m1 and 1 arre 5

Step-by-step explanation:

Answer: CA

Step-by-step explanation:

corresponding angles

90=5x

x=18

m1=90

m2=90

Kenny had 24 pairs of socks before she went on vacation. After vacation she only had 18 pairs. What is the percent decrease of socks from before until after vacation

Answers

Answer:

Step-by-step explanation:

25% decrease

a car travels at a speed of 25 miles per hour. the distance it travels in h hours given by the equation d(h)=25h.
estimate how far he will be 2.5 hours into his trip

Answers

Is there a 62.5 miles option?

The chart below shows Mrs. Thompson's grocery bill. What is the average amount Mrs. Thompson spent on groceries?

A. $58
B. $68
C. $78
D. $340

Answers

Answer:$68

Step-by-step explanation:

Add $47+$66+$68+$71+$88. You get $340. Divide this by 5 (because there are 5 weeks). You get $68.

Roll a number cube. If the number cube comes up odd, you win the same number of points as the
number on the cube. If the number comes up even, you lose 4 points.
What is the expected number of points per roll?
-0.25
-0.5
0
Oo oo
0.25
0.5

Answers

Answer:

-0.5

Step-by-step explanation:

Please help me find the area of this!!! 15 points!!

Answers

Answer:

[tex]A\approx1608.7\text{ yards}^2[/tex]

Step-by-step explanation:

We can use the alternate formula for the area of a triangle:

[tex]A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are the side lengths, and C is the angle between the side lengths.

We know that one side length is 60 and the other is 70.

The angle between them is 50°.

So, substitute 60 for a, 70 for b, and 50° for C. This yields:

[tex]A=\frac{1}{2}(60)(70)\sin(50)[/tex]

Evaluate using a calculator. Make sure you’re in Degrees Mode.

Therefore, the approximate area is:

[tex]A\approx1608.7\text{ yards}^2[/tex]

of the students in a school are in sixth grade. a. How many sixth graders are there if the school has 90 students? b. How many sixth graders are there if the school has 27 students? c. If the school has students, write an expression for the number of sixth-graders in terms of. d. How many students are in the school if 42of them are sixth graders? plz help it's my test

Answers

Hiyo! the answer is 20 students :D! so first off we gotta find the exact number of sixth graders, next of when we find the number which is 90, we need to divide or multiply to get our answer. mkay I just noticed there is answer a. b. c .  but I know the exact answer is 20. Sorry if i'm missing something :D

2m - 3 = 13
what is the answer?

Answers

Answer:

m = 8

Step-by-step explanation:

2(8) = 16

16 - 3 = 13

Therefore, m = 8

6. You have 220 feet of fencing material to enclose a rectangular area for your pet animals. Let x = the length of the rectangular enclosure. (a) [7 points] Set up the function A(x) that represent the enclosed area. (b) [7 points] What should be the dimensions of the enclosed area? (c) [2 points] What is the maximum area of the enclosed area?

Answers

Answer:

I will start with (c)

(c) What is the maximum area of the enclosed area?

the maximum area of a rectangle is always given by a square figure

since the square has 4 equal sides, each side will be 220 / 4 = 55 ft long

maximum area = 55 x 55 = 3,025 ft²

(b) What should be the dimensions of the enclosed area?

the dimensions would be 55 ft in length by 55 ft in width

(a) Set up the function A(x) that represent the enclosed area.

perimeter of the rectangle = 220

we have 4 equal sides, so

A(x) = x²

In 1-4, write an equation in slope-intercept form to represent each table (just the first 4)

Answers

Answer:

Q1 y = 17/2x - 2

Q2 y = -3x + 14

Q3 y = 1/4x

Q4 y = 1/8x + 10

Step-by-step explanation:

See, the problem here is, you did everything to NOT convert the decimals into fractions. You would´ve had the right answers if you just learned to deal with the fractions. I´ll only going to be explaining 2 questions since there´s four of them.

Question Two

You take two points from the table, then you do y2 - y1 over x2 - x1.  -1 - 5 / 6 - 3 = -6/3 and 3 divided by -6 is -3. Which should give you "m" the slope. Which the slope for this question is -3. To find "b" our y-intercept, we will need to plug in the points from one of the two points we took in the chart into the format of y = mx + b. I chose to do, 5 = -3(3) + b. Multiply m times the x, 5 = - 9 + b. So now, we add 9 to itself to cancel itself out and add it to 5. Which gives us, 14 = b. So our equation is, y = -3x + 14

Question 3

This one is relatively easy, since looking at the table we know theres no b or m. Just a constant rate times x. The same thing we did the last question, take two points from the equation. y2 - y1 over x2 - x1. 1 - 0 over 4 - 0. Which gives us 1/4. 1/4 is our constant rate of change. y = 1/4x

The equation in slope intercept form to represent each table is

Q1 y = 17/2x - 2  Q2 y = -3x + 14  Q3 y = 1/4x   Q4 y = 1/8x + 10

What is slope intercept form ?You ought to be familiar with two-variable linear equations. You should specifically be aware that the graph of these equations is a line. Check out our introduction to two-variable equations if this is new to you.Additionally, you should be knowledgeable with the y-intercept, x-intercept, and slope of linear equations.Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.Q2 : Then, you apply y2 - y1 over x2 - x1 over the two points you took from the table. In other words, 3 divided by -6 is equal to -3. This ought to give you the slope "m". Which means that this question has a slope of -3. We must enter the points from one of the two points we picked from the chart into the formula y = mx + b in order to determine "b," our y-intercept. I decided to do 5 = -3 (3) + b. 5 = - 9 + b when the x is multiplied by m. Thus, we add 9 to itself in order for it to cancel out and then add it to 5. The result is that 14 = b. Our equation is therefore y = -3x + 14.Q3 : This one is quite simple because it is obvious from the table that there is no b or m. just a fixed rate multiplied by x. Take two points out of the calculation, just like we did with the previous question. Over x2 - x1 is y2 - y1. 1 - 0 over 4 - 0. thereby giving us 1/4. Our constant rate of change is 1/4. y = 1/4x

Learn more about Slope intercept form refer :

https://brainly.com/question/24907633

#SPJ2

What up guys it’s JustinExpert I’m new if you want to learn more follow you don’t have to do it though but I’m assuming ima be popalar so yeah I will be posting nice content

Answers

Answer:

okay

:)

Step-by-step explanation:

Answer:

wow cool good luck but maybe change your name if you want to be popular

Point: (3,−4)

m: −1

Equation:
please answer will mark brainlest need the equation answer in 1 hour

Answers

Answer:

We need to turn the equation into y=mx+b form.

So the equation would be:

y=-1(3)+-4

Step-by-step explanation:

Multiply : 1 2/5 x 1/4

Answers

Answer:

0.35

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

1 2/5 ×1/4=7/20

It takes 6 cubes to build a staircase with 3 steps. How many cubes will be needed for 11 steps?

Pls show work

Answers

Answer:

5 more cubes

Step-by-step explanation:

you just keep on adding the cubes. So i am in honors math and the easiest way to do math like this just use paper so start with the number of cubes and the just keep on adding till you get to the number you need in this case that number is 11.

I need help with this problem someone please help me

Answers

Answer:

67

180-46=134

134/2=67

I’m not sure but good luck

doing my sister's homework plz help

Answers

Answer:

5/14

Step-by-step explanation:

(Proportional Relationships)

At a certain elementary school there are 26 students per
classroom. If y represents the total number of students at
the school and x represents the number of classrooms,
which equation is the best representation?

Select one:

y = 26/x

y = 26x

x = 26y

y = 1/26 x

Answers

Answer: y =26x

Step-by-step explanation:

A camera is able to capture 3/4 of a picture per second. How long will it take a camera to snap 6 pictures

Answers

It would take 8 seconds. Branliest? :)

solve for x 3(x-8) = -29.7

Answers

Answer:

[tex]x = - 1.9 [/tex]

The answer of this equation is:

1.9

What is - ( 2)^3?


Help please

Answers

Answer is -8

-2x2x2:-8

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Angle A: (5x – 5) degrees

Angle B: (3x + 3) degrees

Angle C: (5x) degrees

The sum of the measures of the three angles is equal to 180°. What is the measure of Angle B?

Answers

Answer:

I don't know i am new

Step-by-step explanation:

Sorry

Daniel baked 12 pies in 6 days Rates

Answers

That’s too much Pie and it’s waste a lot of money yooo and why would he do that dang wow :(
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