John hit a golf ball from the ground and it followed the projectile h(t)=-16t²+100t+0, where is the time in seconds, and ℎ is the height of the ball. Use the quadratic formula to solve the two roots. These represent the 2 times that the ball is on the ground. At what time does the golf ball land? What is the max height of the golf ball? At what time (t) is the golf ball at the maximum height?

Answers

Answer 1

Answer:

The maximum height of the golf ball h(t) = 156.25m

The maximum height of the golf ball at  t = 3.125 seconds

Step-by-step explanation:

Step(i):-

Given

                 h(t)=-16t²+100t   ...(i)

Differentiating equation (i) with respective to 't'

              [tex]\frac{dh}{dt} = -16(2t) + 100 (1)[/tex]

              -32t + 100 =0

            ⇒ -32 t = -100

           [tex]t = \frac{100}{32} = \frac{25}{8} = 3.125[/tex]  

         t = 3.125 > 0

Step(ii):-

 Given h(t) = -16t²+100t  = 0

t ( -16 t + 100 ) =0

t =0 and  -16t = -100

t =0 and  t = 6.25

Step(iii):-

             h(t) = -16t²+100t ...(i)

put t=0  in equation (i)

           h(0) = 0

put t = 3.125 in equation (i)

h(t) = -16(3.125)²+100(3.125)

         h (t) =  156.25

Put t = 6.25

h(t) = -16(6.25)²+100(6.25)

    = 0

The maximum value h(t) = 156.25 at 3.125

final answer:-

The maximum height of the golf ball h(t) = 156.25m

The maximum height of the golf ball at  t = 3.125 seconds


Related Questions

11

Which correctly explains how to use place value and the distributive property to find the product of 742 and

Answers

Answer:

6678

Step-by-step explanation:

742 = 700+40+2

(700+40+2)*9 = 700*9+40*9+2*9 = 6300+360+18 = 6678

Answer:

D Write 742 as 700 + 40 + 2. Multiply each addend by 9. Then add the three products to get 6,678.

Step-by-step explanation:

I did the math >:3

sorry if it's wrong

ANSWER QUICK I WILL GIVE BARINLIEST URGENT

Answers

Answer:

27/40

Step-by-step explanation:

Answer:

3/8 divided by 5/9 = 0.675

Step-by-step explanation:

in fraction form = i dont know srry =/

An item is regularly priced at $43. Charmaine bought it at a discount of 95% off the regular price. How much did Charmaine pay?​

Answers

Answer:

Charmaine paid $2.15

Step-by-step explanation:

So Charmaine only paid for 5% of the regular price

5/100×$43=5×$0.43

=$2.15

Answer:

2.15$

Step-by-step explanation:

95% of 43 is 40.85

43 - 40.85 = 2.15

Nels works 8 hours and earns $52. How many hours would he have to work to earn $130?

Answers

Answer:

20 hours

Step-by-step explanation:

52/8 = $6.5/hour

130 / 6.5 = 20

20 hours

A box without cover is to be constructed from a rectangular cardboard measuring 6 cm by 10 cm by cutting out four square corners of length x cm. Let V represent the volume of the box. Express the volume V of the box in terms of x, writing the equation in factored form.

Answers

Answer:

60xcm^3

Step-by-step explanation:

6 times 10 times x

60x

Someone please do this!

Answers

Answer:

£518.42

Step-by-step explanation:

518.42 I think that’s right

The company that owns the telescope gives a discount of $8 off the rental fee for every rental hour after the first two hours. The team of three astronomers will rent the telescope for 5 hours.

A company interested in the astronomers' research has agreed to pay for 40% of the telescope rental costs. If the astronomers divide up the remaining costs evenly, how much will each of them pay for the 5 hours of rental time?

Answers

Answer:

20

Step-by-step explanation:Please give me a brainly

Angelinas grandfather gave her all the money he had in his pocket to buy. A raffle ticket that coast $1 each for her cheerleading fundraiser determine the independent quantity and the dependent quantity in the problem situation

Answers

Answer

independent quantity is the raffle tickets and the dependent is the amount of money

Step-by-step explanation: i believe im sorry if this is wrong

Luci Lulu opened a cookie store in the mall. She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship x = −2000 p + 4000 . Find the maximum revenue Luci can make selling cookies in one day. Find the price she should sell the cookies for to make the maximum revenue.

Answers

Answer:

The price to make maximum revenue is 1 and the maximum revenue is 2000.

Step-by-step explanation:

Consider the provided information.

Revenue is the product of the number of sales and the sales price.

Here, [tex]p[/tex] is the price of a cookie and the number of cookies sold is [tex]x =- 2000 p + 4000[/tex].

[tex]\text{Revenue}=p(-2000 p + 4000)[/tex]

[tex]\text{Revenue}=-2000 p^2 + 4000p[/tex]

The above equation is a quadratic equation and the graph of the above equation will be a downward parabola because the coefficient of [tex]p[/tex] is negative.

The vertex(axis of symmetry) of a downward parabola has the maximum point.

The axis of symmetry is  [tex]x=\frac{-b}{2a}[/tex]  for the quadratic equation [tex]ax^2+bx+c=0[/tex].

By compare Revenue equation with [tex]ax^2+bx+c=0[/tex], we get:

[tex]x=p, a=-2000, b=4000 \text{ and } c=0[/tex]

Now put the respective values in the formula [tex]x=\frac{-b}{2a}[/tex] .

[tex]p=\frac{-4000}{2(-2000)}[/tex]

[tex]p=1[/tex]

So revenue will be maximum for [tex]p=1[/tex].

Now put [tex]p=1[/tex] in [tex]\text{Revenue}=-2000 p^2 + 4000p[/tex]

[tex]\text{Revenue}=-2000 (1)^2 + 4000(1)[/tex]

[tex]\text{Revenue}=-2000 + 4000[/tex]

[tex]\text{Revenue}=2000[/tex]

Hence, the price to make maximum revenue is 1 and the maximum revenue is 2000.

Maximum revenue generated = $2000

Price at which the maximum revenue is generated = $1

Maximization of the revenue:

Steps to find the maximum revenue,

Find the equation for the revenue generated.Find the derivative of the expression for revenue and equate it to zero.Find the value of the variable and substitute it in the expression for the revenue generated.

Given in the question,

Price of one cookie = p    Linear relationship between the number of cookies sold 'x' and price of a cookie 'p',

        x = -2000p + 4000

Expression for the revenue generated = Price of one cookie × Number of cookies sold

R = p(-2000p + 4000)

R = -2000p² + 4000p

For the maximum revenue,

"Find the derivative of the expression for revenue and equate it to zero"

R' = -4000p + 4000 = 0

4000p = 4000

p = $1

For p = 1,

R = -2000(1) + 4000

R = $2000

       Therefore, for the price of one cookie as $1, maximum revenue generated will be $2000.

Learn more about the maximization here,

https://brainly.com/question/11859895?referrer=searchResults

Function A and Function B are linear Functions. Function A is represented by the equation
y= -2x+w. Function B is represented by the graph. Which statement is true?
A. The slope of function A is the same as the slope of Function B.
B. The slope of Function A is negative and the slope of Function B is positive.
C. The slope of Function A and B are both positive.
D. The slope of Function A and B are both negative.
Function B
Function A
y = -2x+3
1
2
7
Your answer

Answers

Answer:

6.0 and the other things that you want me on my way 6.0 and if I can

Answer:

I think it is 6.0

Step-by-step explanation:

Hope this helped have an amazing day/month/year!

Which example does NOT show the commutative property of addition? 4+x=x+4
Ab=ba
A+b=b+a
3x+4y=4y+3x

plz answer quick

Answers

Answer:

Ab=ba that one is multiplication I believe

Based on the information given in the diagram, choose all of the statements that are correct.

Answers

Answer:

i think its the last one

Step-by-step explanation:

i think its the last on ig

The true statements from the given statements are -

∠MNP  <   ∠ONP NP ≅ NPOP > PM

What are congruent triangles?

Two triangles are congruent when they have exactly the same three sides and exactly the same three angles.

Given is a triangle as shown in the image.

It is clear that the measure of ∠MNP is less than ∠ONP as

∠MNP = 38°  <   ∠ONP = 39°

The line NP ≅ NP as it is common to both sub - triangles and has same length.

OP > PM since ∠ONP = 39° > ∠MNP = 38°

Therefore, the true statements from the given statements are -

∠MNP  <   ∠ONP NP ≅ NPOP > PM

To solve more questions on congruent triangles, visit the link below-

https://brainly.com/question/27848509

#SPJ6

Find the area of the figure. Use 3.14 for it.
2 ft.
8 ft
3 ft
4 ft
3 ft
8 ft
The area of the figure is I
ft.

Answers

Answer:

0.5 X 2 X 3 = 3

0.5 X 3 X 3 = 4.5

8 X 4 = 32

32 + 4.5 + 3 = 39.5 square ft

This is my last question!! I need help

Answers

Answer:

c) 533

Step-by-step explanation:

Use the trigonometry theorem

tan10°= 94/x

x=533

The answer of this question is C 533

a bus traveled for 540 miles in 12 hours. was it traveling at a faster or slower rate than the car? show your work to explain

Answers

how fast is the car going??? cuz the bus is going 45 mph

Answer:

It is at 45. So you need to determine is it faster of slower. You didn't put the whole question.

Step-by-step explanation:

Write a linear function f with f (5) = -1 and f(0) = -5.
f(x)=____

Answers

Answer:

We conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be:

f(x) = 4/5x - 5

Step-by-step explanation:

Given

f(5) = -1f(0) = -5

f(5) = -1 means at x = 5, y = -1

Hence, the point (5, -1) lies on the line function.

f(0) = -5 means at x = 0, y = -5

Hence, the point (0, -5) lies on the line function.

Thus, the two points on the linear line function graph are:

(5, -1)(0, -5)

Finding the slope between the points (5, -1) and (0, -5)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)[/tex]

[tex]m=\frac{-5-\left(-1\right)}{0-5}[/tex]

[tex]m=\frac{4}{5}[/tex]

The slope-intercept form of the linear line function

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept

We have already determined the slope which is: m = 4/5

We know the y-intercept can be determined by setting x = 0 and solving for y.

Thus, the point (0, -5) represents the y-intercept b = -5.

Now, substituting m = 4/5 and b = -5 in the slope-intercept form

[tex]y = mx+b[/tex]

y = 4/5x + (-5)

y = 4/5x - 5

Therefore, we conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be:

f(x) = 4/5x - 5

in the exponential equation y=2(3)x, what is the value of x when y=18​

Answers

okay, 18=2(3)x, so 18=6x. 18/6=6x/6, so..

when y is 18, x is 3

Answer: X= 2

Step-by-step explanation:

if you substitute the options witht the x in the equation. 2 is the only one that has 18 as the result.


Which point is located at 2/4 on the number line??

Answers

Answer:

on C

Step-by-step explanation:

The point K is located at 2/4.

What is fraction?

"It is a number expressed as a quotient, in which a numerator is divided by a denominator."

For given example,

We have been given a fraction 2/4.

We simplify given fraction 2/4 as

2/4

= 1/2

=0.5

Also, the midpoint of 0 and 1 is,

(0 + 1)/2 = 0.5

In the given graph the midpoint of  0 and 1 is denoted by K

Therefore, the point K is located at 2/4.

Learn more about fraction here:

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Which equation shows the result of substituting and expression for y from the first equation into the second equation for the given system {y=x+5 {y-2x=2

Answers

Answer:

x-2x = -3 and x = 3

Step-by-step explanation:

Given the expression

y=x+5.... 1

y-2x=2.... 2

Substituting the first equation into the second we will have;

From 2;

y -2x = 2

x+5-2x = 2

x-2x +5 = 2

x-2x = 2-5

x-2x = -3

-x =-3

x =3

Hence the required equation is x-2x = -3 and x = 3

Answer:

(x + 5) – 2x = 2

Step-by-step explanation:

Edge 2021

Annie rounds 280.05 to the nearest hundred.

Bobby rounds 280.05 to the nearest ten.

Ciro rounds 280.05 to the nearest integer.

Denise rounds 280.05 to the nearest tenth.

What is the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer?

Answers

Answer: 280.1

Step-by-step explanation: so the reason this is right is because any number under 5 would round it down but 5 and up and it would round up.


What is the coefficient in the expression below?
7b + 10

Answers

Answer:

7

Step-by-step explanation:

a coefficient is is the number being multiplied by the variable, and in this case 7 is being mulitiplied by b, making it the coefficient.

Answer:

Equation : 7b+10

Therefore, cofficient of b is 7

7 is the right answer.

need help on math plz help​

Answers

Answer:

C=304

Step-by-step explanation:

4cups everyday

elephants eat 74×

its 4×74=304

Answer:

4 x 76 = c; c = 304

Step-by-step explanation:

Hope this helps! :)

Let me know if I'm wrong.

All you got to do is answer question means 4, 5, 7, 8! Basically all you Gotta do is read the sentence and then match it with one of the equations to the right that aren’t crossed off, !

4?
5?
7?
8?

Answers

There's no picture to it.

-8 - 4 = -2 + n - 6 - 8n please I need the answer

Answers

N = 4/7 or N = 0.571428

Please help me im stuck and the selected answer is not wrong or right i dont know

Answers

No these triangles are not similar.

Step-by-step explanation:

Given Information on First triangle :

Base = 3

Height = 8

Given information on Second triangle :

Base = 4

Height = 10

Area of a Right Angle triangle :

[tex] \frac{base \times height}{2} [/tex]

Area of First triangle :

[tex] \frac{3 \times 8}{2} = \frac{24}{2} \\ \\ = 12[/tex]

Area of Second triangle :

[tex] \frac{4 \times 10}{2} = \frac{40}{2} = 20[/tex]

Their Ratio :

[tex]12:20 = \frac{12}{20} \\ = \frac{3}{5} [/tex]

So I guess no, the triangles are not similar.

An architect builds a model of a park in the shape of a rectangle. The model is 40.64 centimeters long and 66.04 centimeters wide. One inch equals 2.54 centimeters. Use the ratio table to find the ratio of the length to the sum of the length and width in inches and in simplest form.

Answers

Answer:8: 21

Step-by-step explanation:

Given : An architect builds a model of a park in the shape of a rectangle. The length of the model = 40.64 centimeters

The width of the model = 66.04 centimeters

Since, .

Then ,

Now, the  length of the model =

The width of the model =  

Sum of length and width = 16+26=42 inches

Now, the ratio of the length to the sum of the length and width in inches :_

Hence, the ratio of the length to the sum of the length and width in inches  in simplest form = 8:21

JUAN IS GOD GOD ID JUAN

Find the missing values in the ratio table. Then write the equivalent ratios.

Forks 16 8 _
Spoons 10 _ 30

Answers

Answer:

the missing blank for forks is 0 and the missing blank for spoons is 20

Step-by-step explanation:

If each soda sells for $2.50, what is the expected daily total dollar amount taken in by the vendor from the sale of sodas?

Answers

Answer:

$34.38

Step-by-step explanation:

Y: A random variable that indicates the amount of money that the seller will receive.

p=2,50$

if  x=0  →  y=0.2,50=0$

if  x=5  →  y=5.2,50  = 12,5  $

if  x=10  →  y=10.2,50= 25$

if  x=15  →  y=15.2,50=  37,5$

if  x=20  →  y=20.2,50=  50  $

if  x=25  →  y=25.2,50=  62,5$

Y=  { 0$ ; 12,5$ ; 25$ ; 37,5$ ; 50$ ; 62,5$ }

E(Y)=  ∑Y.P(Y)

=  0.P(0)+12,5.P(12,5)+  25.P(25)+  37,5.P(37,5)+  50.P(50)+  62,5.P(62,5)

=  0.0,01+  12,5.0,15+  25.0,25+  37,5.0,3+  50.0,25+  62,5.0,04

= 0 + 1,875 + 6,25 + 11,25 + 12,5 + 2,5

= 34,38$ expected value of the amount of money the seller receives.

Find the annual infiltration rate for the nearest 10th of a percent of a gallon of milk that increases the value from $1.51 to $2.03 over a period of seven years.

Answers

Answer:

7.429 cents

Step-by-step explanation:

Given that:

Price change = $1.51 to $2.03

Period of time = 7 years

Therefore, the annual inflation rate :

Difference in price / number of years

($2.03 - $1.51) / 7

$0.52 / 7

= 0.0742857 per year

= 0.0742857 * 100 (about 7.429 cents per year)

The domain of f(x) = 4x is

The range of f(x) = 4* is

Answers

Answer:

Domain:

-∞ < x > ∞

Range:

-∞ < y > ∞

Step-by-step explanation:

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