A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ft/sec. The function s(t)=−16t2+20t+3 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

Answers

Answer 1

Answer:

[tex]t=\frac{5}{8}s[/tex] and [tex]s(\frac{5}{8})=\frac{37}{4}ft[/tex]

Step-by-step explanation:

There are different approaches you can take to solve this problem. You can look at it from the geometric approach or the calculus approach. I will us the geometric approach.

When we analyze the given function for the height of the ball:

[tex]s(t)=-16t^2+20t+3[/tex]

we can see that we are dealing with a quadratic function. This means that the graph will be an inverted parabola, just like the one in the attached picture.

so the idea is to find the vertex of the parabola to find the highest the ball gets to be and the time it gets to be at that height.

In order to do so, we can use the vertex formula, which looks like this:

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

this is use when you have a function with the form:

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

in this case:

a=-16, b=20 and c=3, so the formula then turns to:

[tex]t=-\frac{20}{2(-16)}[/tex]

which yields:

[tex]t=\frac{5}{8} s[/tex]

which is our first answer. So we can then use this to find the maximum height of the ball, just by substituting t into the original function:

[tex]s(\frac{5}{8})=-16(\frac{5}{8})^2+20(\frac{5}{8})+3[/tex]

which yields:

[tex]s(\frac{5}{8})=\frac{37}{4} ft[/tex]

which is our second answer.

A Ball Is Thrown Directly Upward From A Height Of 3 Ft With An Initial Velocity Of 20 Ft/sec. The Function

Related Questions

ben payed $900 for a sofa. The price of the sofa Juana was 2/3 the price ben payed. How much did Juana pay for her sofa?

Answers

Answer: $600

Step-by-step explanation:

Find 2/3 of $900.

To do this, we have to get 9 and divide by 3.

9 ÷ 3 = 3

Multiply 3 by 2. You get 6.

Add two zeros.

You will get $600.

A power boat travels along a river in which the flow of water is at a constant in one direction. If the boat travels at 40 mph downstream and 30 mph upstream. What is the speed of the boat in still water and the speed of the river?

Answers

Answer:

speed of boat is 35 mph

speed of river is 5mph.

Step-by-step explanation:

Let the speed of boat be u mph

let the speed of river be v mph

When boat travel downstream

in that case flow of river will support the speed of boat hence

speed of river will be added to speed of boat

Thus,

speed of boat in downstream = speed of boat + speed of river = u + v

Given

the boat travels at 40 mph downstream

thus,

u + v = 40 -----1

When boat travel upstream

in that case flow of river will oppose the speed of boat hence

speed of river will be subtracted from speed of boat

Thus,

speed of boat in downstream = speed of boat -speed of river = u - v

Given

the boat travels at 30 mph upstream

thus,

u - v = 30 ----2

adding 1 + 2

we have

u + v = 40

+ u - v = 30

2u = 70

u = 70/2 = 35

Thus,

speed of boat is 35 mph

using u = 35 in u + v = 40

we have

35 + v = 40

v = 40 - 35 = 5

Thus, speed of river is 5mph.

please can you help. i would really appreciate it

Answers

Answer:

The integers that satisfy both inequalities are any number between -4.5 and -12

Step-by-step explanation:

Hope this helps and pls do mark me brainliest if you can:)

Circle A has a diameter of 9 , Circle B has a radius of 5 , how many centimeters larger is it ?

Answers

Answer:

Step-by-step explanation:

A speedboat, at full throttle, can go 65.0 miles in 1.5 hours. What is the average speed of the boat?

Answers

the average speed is about 40

bbs.
Which statement best compares the two jobs?
O Job A has a lower salary than job B, but the benefits
make job A a more attractive pay package.
O Job B has a lower salary than job A, but the benefits
make job B a more attractive pay package.
O Job A has a higher salary than job B plus benefits that
make job A a more attractive pay package.
O Job B has a higher salary than job A plus benefits that
make job B a more attractive pay package.

Answers

Answer:

B - Job B has a lower salary than job A, but the benefits

make job B a more attractive pay package.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

is 54/35 a rational number?

Answers

Answer:

54/35 is a rational number!

Have a great rest of your day!

Answer:

Yes and no

Step-by-step explanation:

The number 54 is a rational number if 54 can be expressed as a ratio, as in Rational. A quotient is the result you get when you divide one number by another number. Although the 54 is good the 35 is not due to it if you had to choose if it was or not you can say yes but it determines the question.

even number less than 12

Answers

Answer:

2,4,6,8,10

Step-by-step explanation:

they are even numbers

Answer: 2, 4, 6, 8, 10

Step-by-step explanation:

any of those are even numbers that are less than 12

Express the ratio below in its
simplest form.
18:3:9

Answers

Answer:

6:1:3

Step-by-step explanation:

A LOT OF POINTSS

find the surface area

Answers

Answer:

He used 286.73² in. of wrapping paper.

Answer:

I got 286.73

Step-by-step explanation:

I found the area of all the shapes in the thing and added them.

Pls correct me if I did the adding wrong cuz its 55+20+20+88+103.73

If k(x) = -2x2 – 7, find k(4)

Answers

Answer:

-39

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

You just plug in 4 for x. So it'd be -2(4)2-7

So, you have -8(2)-7

Then: -16-7, which gives you -23

hans cellphone plan costs $200 to start. Then there is a $50 charge each month

Answers

Y=200+50x and x is how many months

2x+5y=10
Solve for y

Answers

2x+5y=10

Move constant to the left by adding its opposite to both sides

2x+5y-10=10-10

the sum of two opposites equals 0

Answer: 2x+5y-10=0

PLEASE MARK ME AS BRAINLIEST

A local charity collected 163 cans of food
every day for 14 days. How many cans did they collect
in the first 10 days? How many did they collect in the
remaining 4 days? How many cans did they collect in
all? Solve this problem any way you choose!

Answers

Answer:

This was $14 less than twice what she spent for a blouse . How much ... From the first two equations, we have A=12B=12(3C)=32C ... How many days will it require for the son to plow the field alone?

Step-by-step explanation:

Which equation represents the line that is parallel to 5x +y = 13 and passes through the point (15,-31)? Show complete working format please

Answers

Answer:

Step-by-step explanation:

y = -5x + 13

y + 31 = -5(x - 15)

y + 31 = -5x + 75

y = -5x + 44

Consider the pairs of ratios given and determine whether or not the ratios form a proportion 8 old rings for every 1 ring 16 old rings for every 2 rings A) Yes B) No Save

Answers

Answer:

Step-by-step explanation:

31 SPORTS Sixteen students in Mr. Prank's gym class each
participate in one or more sports as shown in the
table. Examples 2 and 3
Mr. Frank's Gym Class
Basketball Soccer Volleyball
Ayanna Lisa Pam
Ayanna Lisa
Sue
Pion
Shin
Lisa Tyron Mex
Ron
Max
Alda
Max
Aida
Juan
Ito
Evita
Juan
Nela
Percy
Tino
Kai
Percy
Nella
a. Let B represent the set of basketball players, S
represent the set of soccer players, and V represent the
set of volleyball players. Draw a Venn diagram of this
situation.
b. Find Sn V. What does this set represent?
c. Find S. What does this set represent?
d. Find BUV. What does this set represent?

Answers

A. Correct answer...................

Nadia charges $5.50 an hour for babysitting. She babysits 17.50 hours the first week of the month and 21 hours the second week of the month.

Suppose Nadia raises her rate by $0.55 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month?

Answers

Answer:

about 34 hours

Step-by-step explanation:

Answer:

35 hours.

Step-by-step explanation:

To achieve an answer to this question, we'll have to set two expressions equal to each other.

Let's first start by calculating how much Nadia has made in the first two weeks of the month. We can do this by adding the amount of hours she works in the first and second week together:

[tex]21+17.5[/tex]

[tex]=38.5[/tex]

Let [tex]h[/tex] equal hours.

Set up your first expression:

[tex]5.50h[/tex]

Let's go ahead and substitute 38.5 into the expression to see how much money she will make the first two weeks of the month at a rate of $5.50 an hour:

[tex]5.50(38.5)[/tex]

[tex]=211.75[/tex]

We are told that Nadia raises her rate by $0.55, so we'll need to add 0.55 to 5.50 in order to find her increased rate:

[tex]5.50+0.55[/tex]

[tex]=6.05[/tex]

Set up your second expression:

[tex]6.05h[/tex]

Now, set this equal to how much she made the first two weeks at a rate of $5.50 an hour:

[tex]211.75=6.05h[/tex]

Divide both sides of the equation by the coefficient of [tex]h[/tex], which is [tex]6.05[/tex]:

[tex]35=h[/tex]

Therefore, it will take Nadia 35 hours to earn the same amount of money she made in the first two weeks of the month.

Check your work by substituting 35 for [tex]h[/tex] in the equation below:

[tex]211.75=6.05h[/tex]

[tex]211.75=6.05(35)[/tex]

[tex]211.75=211.75[/tex]

Since both sides of the equation are equal to each other, our answer is correct!

4. Write an equation for the table in slope intercept form

Answers

Answer:

y=1.6x-5

Step-by-step explanation:

all you need is in the photo

Answers

Answer:

slope is -1, y intercept is 5

Step-by-step explanation:

slope formula is y1-y2 over x1-x2

plug in formula

u get the slope is -1

Answers:

Slope = 4

Y intercept = 5

======================================================

Explanation:

Start at the point (-1,1) which is one point on the line. Then move up 4 units and to the right 1 unit to get to (0,5). This is another point on the line.

Therefore the slope = rise/run = 4/1 = 4.

You could also use the slope formula m = (y2-y1)/(x2-x1)

---------------

The y intercept is 5 since the line crosses the y axis at this location. More specifically this is the point (0,5). For any y intercept, x = 0.

The equation of this line in slope intercept form is y = 4x+5. Compare it to y = mx+b and we have m = 4 as the slope and b = 5 as the y intercept.

ario made a deposit in an account that earns annual interest. His account balance, in dollars, after t years is represented by the expression 400⋅1.05t . Yvonne made a deposit in an account that earns annual interest. Her account balance, in dollars, after t years is represented by the expression 300⋅1.06t . Which statement describes the situation correctly? A. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent more annual interest than Mario’s account. B. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent less annual interest than Yvonne’s account. C. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent less annual interest than Mario’s account. D. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent more annual interest than Yvonne’s account.

Answers

Answer:

nothing at all.

Step-by-step explanation:

Solve the system, by elimination please show all the steps!
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answers

Answer:

x = 1 , y = 1 , z = 0

Step-by-step explanation:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

-2 x - y + z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2: