S(t) = -16t^2+96t+256 the quadratic function models the balls height above the ground, s(t), in feet, t seconds after it was thrown when a person standing close to the edge on top of a 248-foot building throws a baseball ball vertically upward. When will the ball reach its maximum height, and what is the maximum height of the ball?

Answers

Answer 1

Answer:

The ball reaches maximum height in 3 seconds.

The maximum height of the ball is of 400 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

In this question:

The height is modeled by:

[tex]s(t) = -16t^2 + 96t + 256[/tex]

So, the coefficients are:

[tex]a = -16, b = 96, c = 256[/tex]

Instant of time the ball reaches maximum height:

[tex]t_{v} = -\frac{96}{2(-16)} = -\frac{96}{-32} = 3[/tex]

The ball reaches maximum height in 3 seconds.

What is the maximum height of the ball?

This is s(3).

[tex]s(3) = -16t^2 + 96t + 256 = -16*3^2 + 96*3 + 256 = 400[/tex]

The maximum height of the ball is of 400 feet.


Related Questions

A new watch costs $38.85, and a new bracelet costs $22.38. If Maddy buys both, how much does she spend?

Answers

Answer:

$61.23

Explanation:

$38.85 + $22.38 = $61.23

Answer:

maddy will spend $61.23

Step-by-step explanation:

add $22.38 to $38.85

8th grade teachers and students from M.I.T went on a field trip to an zoo. Tickets
were $5.00 each for teachers and$3.50 each for students, and the group paid
$51.50 in total.A few weeks later, the same group visited a natural history
museum where the tickets cost $20.00 each for teachers and $8.50 each for
students, and the group paid $156.50 in total.
Find the number of teachers and students on the field trips.
A 4 Teachers and 9 Students
4 Teachers and 10 Students
3 Teachers and 9 Students
D None of the above

Answers

As there are multiple answers going with trial and error seems good in this case.

A

5.00 + 5.00 + 5.00 + 5.00 = 20.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 31.5

20.00 + 31.5 = 51.5

B

5.00 + 5.00 + 5.00 + 5.00 = 20.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 35.00

20.00 + 35.00 = 55.00

C

5.00 + 5.00 + 5.00 = 15.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 31.5

15.00 + 31.5 =46.5

Knowing that for the first one all A,B, and C were wrong we can determine that D is the answer. But wait if I made one mistake and didn't understand if $156.5 is equivalent to $156.50 that would mean A is correct.

Always recheck your answers and good luck,

Jon

75 times 243

If your doing just for points I’ll report you

Answers

18,225 :) have a nice day!
18,225 I hope you have the most amazing day

Which Question is equivalent to

Answers

Answer:

[tex]\frac{3}{2}a^{2}|b^{3}|c^{4}[/tex]

Step-by-step explanation:

Answer:

option. b 3/2a²|b³|c⁴

..............

Parker drove 8 miles in 15 minutes. If he drove at a constant rate, how far did he travel in one hour?

Answers

The answer is 32 miles
The Answer is
32 miles

can someone help me plssssss

Answers

Answer:

16.5

Step-by-step explanation:

Someone was shopping at a store that advertised 50% off everything. She found a new CD player originally priced at $76. What was the sale price?

Answers

Answer:

38

Step-by-step explanation:

Please help me with this!!!

Answers

Answer:

2x 1

x 2x² x

-2 -4x -2

=> = 2x² - 3x - 2

Answer:

Step-by-step explanation:

Weird question but, whenever you divide by 1/4 or multiply by 4/1, will you always get the same answer.

(25 points if you answer this.)

Answers

Answer:

yep

Step-by-step explanation:

when you divide a fraction u can use the KCF method which is basically:

(keep) the first fraction the same

(change) the division sign in the middle to a multiplication sign

(flip) the second fraction

basically because you have to flip the 1/4 when you divide it, it'll be the same as a 4/1 anyways

The longest side of a triangle is 8 more units than the shortest side. The third side is 4 times the length of the shortest side. If the perimeter of the triangle is 32 units, write and solve an equation to find the length of all 3 sides of the triangle

Answers

Answer:

10 3/4, 4 3/4, and 9 1/2

Step-by-step explanation:

We're going to let x represent the length of the longest side. The perimeter is

x +(x-6) +2(x-6) = 25

4x -18 = 25

4x = 43

x = 43/4 = 10 3/4

Then x-6 = 4 3/4.

Multiply that two to get 8 3/2 = 9 1/2

I hope this helped! :)

Two vertical posts stand side by side. One post is 8 feet tall while the other is 17 feet tall. If a 24 foot wire is stretched between the tops of the posts, how far apart are the posts?​

Answers

Answer:

22 1/4 feet

Step-by-step explanation:

you can sketch this problem to be a right triangle with a hypotenuse of 24 feet and one leg of 9 feet (17 - 8).

use Pythagorean Theorem to find the base side, which represents the distance between the posts

a² + 9² = 24²

a² + 81 = 576

a² = 576 - 81

a² = 495

a = [tex]\sqrt{495}[/tex]

a = [tex]\sqrt{9}[/tex] · [tex]\sqrt{55}[/tex]  =  3[tex]\sqrt{55}[/tex], which is approx 22.25

Answer:

about 22.25 feet

Step-by-step explanation:

You can think of it like a triangle, which you can see at the bottom

Then, use the pythagorean theorem, [tex]a^2 + b^2 = c^2[/tex].

you have a = 9 and c = 24, so

[tex]9^2 + b^2 = 24^2\\81 + b^2 = 576\\b^2 = 495\\b = \sqrt{495} = 3\sqrt{55} = about 22.25[/tex]

What is the length of AB

Answers

d

Step-by-step explanation:

because that is the answer

The correct answer is D

-5x -2y= -9
8x + 8y= 24

Answers

Answer:

x=5

y=-17

Step-by-step explanation:

basically what I did was:

1) I multiplied the first equation by 4 , solved for x

2) I used the value of x that i found and substituted in one of the equations to find y

Answer: x=0 y=2

..................

The midpoint of overline AB is M(0, - 7) . If coordinates of A are (- 2, - 6) , what are the coordinates of B?

Answers

Given:

The midpoint of overline AB is M(0, - 7) .

The coordinates of A are (- 2, - 6).

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The midpoint of overline AB is M(0, - 7). Using the midpoint formula, we get

[tex]M=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)[/tex]

[tex](0,-7)=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{-2+a}{2}=0[/tex]

[tex]-2+a=0[/tex]

[tex]a=2[/tex]

And,

[tex]\dfrac{-6+b}{2}=-7[/tex]

[tex]-6+b=-14[/tex]

[tex]b=-14+6[/tex]

[tex]b=-8[/tex]

Therefore, the coordinates of point B are (2,-8).

Robert has 6 pints of water to use on 5 plants.
If Robert gives each plant the same amount, how many pints of water will each plant get?
A. 5/6
B. 1
C. 1 1/5
D. 5

Answers

Answer

I think the answer is B)

Step-by-step explanation:

because I subtracted 6 and 5 because Robert has 6 pints of water and there's 5 plants

Please help someone pleaseeeeeeeeeeeeeeeeeeee

Answers

Mean is adding all the numbers then dividing the answer you go from the numbers.

Answer:

first question: decrease - second question: 34

Step-by-step explanation:

first question: to find the mean, you need to add all of the numbers together and divide the sum of those by the amount of numbers you added together. in this question, it would be

73+79+96+84=332 -> 332/4=83 is the mean for the 1st set of numbers

(1)   (2)  (3)   (4)

the question asks what happens after the next test score is added in, for this, you will do the same steps as before except you add in the 80 for her fifth test and then divide by 5 instead of 4, because you have another number being added.

73+79+96+84+80=412 -> 412/5=82.4 is the mean for the 2nd set of numbers

the second set of numbers, after the fifth test score is added in, is lower than the first set of numbers. therefore, the mean decreases

second question: same concept, except on a dot plot. a dot above a number means that there is one of those numbers that should be counted. this means since there are 2 dots above the 30, there are 2 30s being added to the rest of the numbers. in this dot plot, the numbers being added are

30+30+32+32+34+38+38+38=272 -> 272/8=34 is the mean

hope this helps!

pls help meh

6th grade math

Answers

Answer:

1,728%

Step-by-step explanation:

multiply baby

Actually jt is 75% divide 36 by 48

please help! find QPR

Answers

Answer:

m∡QPR = 25°

Step-by-step explanation:

solve for 'x':

8x + 7 + 9x + 16 = 40

17x + 23 = 40

17x = 17

x = 1

m∡QPR = 9(1) + 16

m∡QPR = 25°

The ordered pairs in the table below represent a linear function.

What is the slope of the function?

Answers

Answer:

[tex]\displaystyle m=2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (6, 2)

Point (9, 8)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                            [tex]\displaystyle m=\frac{8-2}{9-6}[/tex][Fraction] Subtract:                                                                                         [tex]\displaystyle m=\frac{6}{3}[/tex][Fraction] Divide:                                                                                            [tex]\displaystyle m=2[/tex]

What is 49/50 equivalent to as a decimal and as a percent

Answers

.98 and98% .................

Select an equation of a parabola that has a vertex at (2,-1) and a zero at x=3 .
A. y=x² -4x+ 5
B. y=x² -4x + 3
C. y=x² + 4x -21
D. y=x² + 4x +3

Answers

The answer to this question is B. y=x^2-4x+3

me podrían decir cuanto es 21/43+8/17 plis​

Answers

Answer:

701/731

Step-by-step explanation:

Espero que ayude

puedes marcarme branliest??

Answer:

701

------- = 0.958960328

731

Step-by-step explanation:

21/43 + 8/17 es

21/43 + 8/17

21      8     701

---- + ----- = -----

43      17     731

50 POINTS

1. Find f(5)
f(x)=x^2-10x+15

2. Find g(x)+f(x)
f(x)=-4x+12
g(x)=3x+5

3. Find f(x)-g(x)
f(x)=-4x+12
g(x)=3x+5

Answers

I know that 1 is -10 but i do not know the rest, sorry!

How many solutions does 15x+12y=18 have

Answers

Answer: 2 or more.

X and Y could be anything, so there are at least two answers

Whats 2/3×(-3) this is multiplication

Answers

Answer: -2

your welcome :)

What's the coefficient of -C.

Answers

Answer:

here we have -C

The Coefficient of -C is -1

i’m just gonna say something because i want points sorry

solve the inequality -5(x-7)<15 algebraically for x.

Answers

x > 4
Hope this helps

Answer:

4

Step-by-step explanation:

1. Divide both sides by -5

2. add 7 to both sides

The total cost of a compact disc, including a 6% sales tax, is $14.31.
What is the price before the tax?
$13.50
$13.45
$13.44
$15.17

Answers

It's 13.50 I'm pretty sure
$13.50 • 1.06 is $14.31

The cost of a compact disc before the sale tax is $13.45. The correct option is B.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the total cost of a compact disc, including a 6% sales tax, is $14.31.

The cost before the sale tax will be calculated as,

Cost = 14.31 x ( 1 - 0.06 )

Cost = 14.31 x 0.94

Cost = $13.45

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ5

The prime factorization of 16x5

Answers

Answer:

well first 16x5=80

2 * 2 * 2 * 2 * 5

Step-by-step explanation:

Hope that helps! :)

Which best describes how to add 9.73 and 21.6

Answers

Answer:

Step-by-step explanation:

9.73

+

21.60

31.33

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