a quarterback throws a ball in the air from an initial height of 5 feet. The football has an initial vertical velocity of 50 feet per second. Another player catches the ball when it is 2 feet above the ground. How long is the ball in the air?

Answers

Answer 1

Answer:

The range of the function is from 2 feet to 12.25 feet

Step-by-step explanation:

In a function f(x) = y

x is the domain of the function

y is the range of the function

The height (h) of the ball at time (t) seconds can be represented by the equation h(t) = - 16 t² + 20 t + 6

∵ h(t) = - 16 t² + 20 t + 6

∴ The domain is t

∴ The range is h(t)

- To find the range of the quadratic function find the maximum or

minimum value of it

∵ The leading coefficient of the function is -16

∴ The function has a maximum value

To find the maximum value differentiate h(t) with respect to t and equate it by 0 to find the value of t for the maximum height

∵ h'(t) = -16(2) t + 20(1)

∴ h'(t) = -32 t + 20

- Equate it by 0

∵ h'(t) = 0

∴ -32 t + 20 = 0

- Subtract 20 from both sides

∴ -32 t = - 20

- Divide both sides by -32

∴ t = 0.625 seconds ⇒ time for the maximum height

Substitute the value of t in h(t) to find the maximum height

∵ h(0.625) = -16(0.625)² + 20(0.625) + 6

∴ h(t) = 12.25 feet

∴ The maximum height of the ball is 12.25 feet

∵ The ball is caught at 2 feet

∴ The range of the function is 2 ≤ h(t) ≤ 12.25

The range of the function is from 2 feet to 12.25 feet


Related Questions

2) 5x 3 x 2
what is the order of operations

Answers

Answer:

PEMDAS

Step-by-step explanation:

parentheses

exponents

multiplication

division

subtraction

5x3x2=30

PEMDAS
Parentheses, exponents, multiplication, division, addition, subtraction

5x3 is first equaling 15
15x2 is next equaling 30
The answer is 30

Can someone answer this question? I will give brainliest to the best response.

Answers

Answer:

working..

Step-by-step explanation:

You bought a magazine for $2 and some erasers for $5 each. You spent a total of $12. How many erasers did you buy?​

Answers

5+2 = 7
Add 5 more (1 more magazine) and the total amount equals 12
So.. bought 2 erasers
You bought 2 erasers, (5+5=10) and $2 on a magazine together (10+2=12), pls give Brainliest!

1. What are the different offensive and defensive strategies that are used in water polo?
2. Which strategies do you think are the most difficult to accomplish? Why?
3. Which strategies do you think are the easiest to achieve? Why?

Answers

Answer:

A defensive way is use all your might to jump when the ball is coming at you, because as you might know is it takes a lot of effert to jump in a pool, the gravity is very strong in the pool! Or if you get the ball you can throw and swing your arm as strong as you can a HIT that ball! You wanna hit it hard so the players on the other side of the pool don’t get the ball,instead it will go over them and you WIN!

Step-by-step explanation:

Hope this helped :)✨

I need to know ASAP! Thanks ^^

Answers

Answer:

PQ=30

Step-by-step explanation:

Knowing that the segment has 3 parts that are 3:1:1 and sum up to 50, you could find how much 1 would equal by finding the total in relation to the ratio (doing 3+1+1) which gets you 5 parts. Then you can divide the total (50) by 5 to figure out how much one part would equal (10). Now, since you know that 1 part is equal to 10 and that PQ is 3 parts, you can find that PQ is equal to 3x10, or 30.

Solve each equation for x. 1.3x + 9x = 6x + 42​

Answers

Answer:

Just use a calcultor...

Step-by-step explanation:

Parallel or perpendicular 3x+5y=10 and 5x-3y=-6

Answers

3x+5y=10 and 5x-3y=-6 is perpendicular.

Which statement is true of the mapping?
PLEASE HELP MEE

Answers

Answer:

C

Step-by-step explanation:

Please help meeeeeee
I need the answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

4x + 6x + y = 180

6x + y = x + 5y

10x + y = 180 ........... (1)

5x - 4y = 0 .............. (2)

(1) - 2 × (2)

y + 8y = 180 ⇒ y = 20

6x + 20 = x + 100 ⇔ 5x = 80 ⇒ x = 16

64° , 116°

Use the graph to find the cost of 8 hats.
Cost of Hats
110
100
90
80
($) 1803
10
8 7 8 10 11
Number of hats
O A. The cost of 8 hats is $7.50.
ООО
B. The cost of 8 hats is $75.00
O C. The cost of 8 hats is $8.00.
PREVIOUS

Answers

Answer:

are you missing a option because for me one option that has the same exact numbers that you mentioned is the cost of 8 hats is 60

Step-by-step explanation:

A curve is such that (dy)/(dx) = 12/(2x + 1) ^ 2 and P(1, 5) is a point on the curve . (i) The normal to the curve at P crosses the x-axis at Q. Find the coordinates of Q (ii) Find the equation of the curve. (iii) A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.3 units per second. Find the rate of increase of the y-coordinate when x=1

Answers

(i) The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate is 1.2 units per second.

(i) By analytical geometry, we know that the slope of a line normal of a curve ([tex]m_{\perp}[/tex]) by the following expression:

[tex]m_{\perp} = - \frac{1}{\frac{dy}{dx} }[/tex] (1)

Where [tex]\frac{dy}{dx}[/tex] is the slope of the line tangent to the curve.

If we know that [tex]x = 1[/tex], then the slope of the normal to the curve is:

[tex]\frac{dy}{dx} = \frac{12}{2\cdot (1)+1}[/tex]

[tex]\frac{dy}{dx} = 4[/tex]

And the slope of a line normal of a curve is:

[tex]m_{\perp} = -\frac{1}{4}[/tex]

By definition of secant curve we calculate the remaining coordinate of the point Q:

[tex]m_{\perp} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (2)

Where:

[tex]x_{P}[/tex], [tex]x_{Q}[/tex] - x-coordinates of points P and Q. [tex]y_{P}, y_{Q}[/tex] - y-coordinates of points P and Q.

If we know that [tex](x_{P}, y_{P}) = (1, 5)[/tex], [tex](x_{Q}, y_{Q}) = (x, 0)[/tex] and [tex]m_{\perp} = -\frac{1}{4}[/tex], then the remaining coordinate of point Q is:

[tex]-\frac{1}{4} = \frac{0-5}{x-1}[/tex]

[tex]-\frac{1}{4}\cdot (x-1) = -5[/tex]

[tex]-\frac{1}{4}\cdot x +\frac{1}{4} = -5[/tex]

[tex]\frac{1}{4}\cdot x = \frac{21}{4}[/tex]

[tex]x = 21[/tex]

The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is derived by separating the variables and integrating the resulting expression:

[tex]dy = \frac{12}{2\cdot x + 1}\,dx[/tex]

[tex]\int\, dy = 6\int {\frac{2\,dx}{2\cdot x + 1} }[/tex]

[tex]\int \, dy = 6\int {\frac{du}{u} }[/tex]

[tex]y = 6\cdot \ln u[/tex]

[tex]y = 6\cdot \ln (2\cdot x + 1)+C[/tex]

And the integration constant is found for [tex](x,y) = (1, 5)[/tex]:

[tex]5 = 6\cdot \ln(2\cdot 1 + 1) + C[/tex]

[tex]C = -1.592[/tex]

The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate by using the differential equation presented in statement and the definition of rate of change:

[tex]\frac{dy}{dt} = \left(\frac{12}{2\cdot x +1}\right)\cdot \frac{dx}{dt}[/tex] (3)

If we know that [tex]\frac{dx}{dt} = 0.3[/tex] and [tex]x = 1[/tex], then the rate of increase of the y-coordinate is:

[tex]\frac{dy}{dt} = \left[\frac{12}{2\cdot (1)+1} \right]\cdot (0.3)[/tex]

[tex]\frac{dy}{dt} = 1.2[/tex]

The rate of increase of the y-coordinate is 1.2 units per second.

To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/25731911

i). The coordinates of Q is equal to:

[tex](x,y) = (21, 0)[/tex]

ii). The equation of the curve is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate when x = 1:

[tex]1.2 units[/tex] per second

i). Using analytical geometry,

[tex]xp[/tex] and [tex]xq[/tex] are the P and Q's x-coordinates.

[tex]yp[/tex] and [tex]yq[/tex] are the P and Q's y-coordinates.

Since ([tex]xp[/tex], [tex]yp[/tex]) = (1,5) and ( [tex]xq[/tex], [tex]yq[/tex]) = [tex](x, 0)[/tex] and m⊥ = - 1/4, the left coordinate of Q's point:-

-1/4 = (0-5)/(x - 1)

∵[tex]x = 21[/tex]

Thus, the coordinates of y = (21, 0)

ii). Through isolating the variables and employing integration:-

[tex]dy = \frac{12}{(2.x + 1)} dx[/tex]

by integration and integration constant (1,5), the equation is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate:

[tex]dy/dt[/tex] = [tex]\frac{(12)}{(2.1 + 1)} .0.3[/tex]

∵ [tex]dy/dt[/tex] [tex]= 1.2[/tex]

Thus, the rate of increase for y-coordinate when x = 1 is 1.2 units per second.

Learn more about "Co-ordinates" here:

brainly.com/question/21902081

PLEASE HELP MEEEEEEEEEEEEEE

Answers

Answer:

y=7/9x-2

Step-by-step explanation:

This is the formula to follow when doing these equations

y=slopex (-/+) y-intercept

if it a negative it a - intercept if it a positive intercept if adding.

find the slope of the graph given below

Answers

Answer:

[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

Can someone please help me with this proof?!

Given: AC and BD bis, each other.

Prove: ABCD is a parallelogram

Answers

Answer:

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

                                                    DX = BX

                                                    m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Step-by-step explanation:

Water begins to slowly leak from David’s water bottle right after he fills it. After 5 minutes, he notices the bottle has 26 ounces of water remaining. After 30 minutes, he notices the bottle has 16 ounces of water remaining. Let x represent the number of minutes that have passed and let y represent the amount of water remaining in the bottle.

a) Without calculating, will the rate of change (slope) for the water bottle be positive or negative? Explain how you know.




b) What is the rate of change (slope) of this situation (in ounces per minute)?





c) Write an equation to model this situation:








d) How much water was in David’s bottle immediately after he filled it?






e) After how many minutes will David’s bottle be completely empty?

Answers

B hope it helps and hope u pass your thing ur doing or whatever u doing

Marsha is driving 600 total miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?
A. 120 miles


B. 240 miles


C. 300 miles


D. 360 miles

Answers

Marsha had driven 240 miles

Isaac has $15,000 in his bank account. Every month he spends $1,000. He does not add money to the account. EN​

Answers

Answer:

Then he has 15 months?

Step-by-step explanation:

you might need to explain your question

y = 6x - 10
y = 2x + 2

Answers

Answer:

1. x= 5/3 or 1.6 and y= -10

2. x= -1 and y= 2

Step-by-step explanation:

1. y= 6x - 10, 0= 6x - 10, -6x= -10, x= 5/3

2. y= 2x + 2, 0= 2x + 2, -2x= 2, x= -1

pls complete it (picture)​

Answers

Answer:

The answer to your question is 24cm.

Step-by-step explanation:

6 multiplyed by 8 equals 48, and 48 divided by 2 equals 24.

Hope I helped. Have a spectacular day! ;)

Which of the following sets of numbers could represent the three sides of a triangle?​

Answers

Answer:

{5, 15, 19}

Step-by-step explanation:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.

Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:

a + b > c

b + c > a

a + c > b

Where a and b are the smaller side lengths, and c is the length of the longest side.

Let's check each set of numbers given to see if any satisfies this condition.

✍️Option 1: {6, 20, 28}

6 + 20 is not greater than 28

20 + 28 > 6

6 + 28 > 20

❌This set of numbers does not represent the sides of a ∆.

✍️Option 2: {4, 11, 15}

4 + 11 = 15

11 + 15 > 4

4 + 15 > 11

❌This set of numbers does not represent the sides of a ∆.

Option 3: {9, 19, 30}

9 + 19 is not greater than 30

19 + 30 > 9

9 + 30 > 19

❌This set of numbers does not represent the sides of a ∆

Option 4: {5, 15, 19}

5 + 15 > 19

15 + 19 > 5

5 + 19 > 15

✅This set of numbers does not represent the sides of a ∆

Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.

Find the number of terms in this polynomial.
-8f^2

Answers

Answer:

3 terms

Step-by-step explanation:

⚠️PLEASE HELP FAST⚠️ Camie and Jorge each begin saving money
for a new computer. Camie saves $5 per
week plus $50 she receives for her birthday.
Jorge saves $7 per week. Which of the
following can be used to find w, the number
of weeks until Jorge has saved at least the
same amount as Camie?
A.7w = 5W + 50
B.50 + 5w < 7w
C.5W + 50 >_7w
D.7W >_5W + 50

Answers

Answer:

The answer is A

Step-by-step explanation:

Camie: $5x + $50 = $55 ( for now/i think)

Jorge: $7x

The  equation to represent  Jorge has saved at least the same amount as Camie is 7w = 5W + 50.

The correct option is (A)

What is equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

Camie saves $5 per week plus $50 she receives for her birthday.

Jorge saves $7 per week.

Now, Jorge have to achieve the same amount as Camie.

let w be the number of weeks.

Then equation can be represented as

7w = 5W + 50

Here 7w is amount by Jorge and 5W + 50 is amount of Camie.

Hence, the equation to represent  Jorge has saved at least the same amount as Camie is 7w = 5W + 50.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ2

Kelly has ¾ of a pie left. She wants to split the pie with 3 of her friends. How much of the pie will each person get?

Answers

Answer:

1/4 od pie.

Step-by-step explanation: So 3/4 divided by 3 is 1/4

find one arithetic means between 2 and 32​

Answers

Answer:

17

Step-by-step explanation:

17 is one arithmetic means between 2 and 32

pleaseeee hurryyy i needd helppp
How many solutions are there for this equation? Why?
2(m+2)=12−6m
Select the option that correctly answers both questions.
a. There is one solution, because the coefficients of the variables on both sides of the equation are the same.
b. There are no solutions, because the coefficients of the variables on both sides of the equation are different.
c .There is one solution, because the coefficients of the variables on both sides of the equation are different.
d. There are no solutions, because the coefficients of the variables on both sides of the equation are the same.

Answers

Answer:

C. There is one solution, because the coefficients of the variables on both sides of the equation are different.

Step-by-step explanation:

The solution is m = 1

~theLocoCoco

If x = -2, what is the value of y, that makes the equation, y = 2x + 3, true? Explain how you know.

Answers

Answer:

Y is equals to negative 1.

Step-by-step explanation:

y = 2x + 3

y =2(-2)+ 3

y =-4+ 3

y=-1


At a restaurant you meal is $20. In addition to the cost of the meal you must pay a 5% sales tax and leave a 15% tip. What is the total
bill?

Answers

20 dollars plus 5% adds a 1 dollar to get 21 dollars then 15% adds 3.15$ to get 24.15&

Which expressions simplify to a rational answer?
Select each correct answer.

Answers

Answer: the answers are the second one and the last one

Step-by-step explanation:

please help ASAP!
i will give brainliest!! :)

Answers

Answer:

its c i took the test trust me

Step-by-step explanation:

The answer is C I took the test and got the answers on side of me

3 + 2p - 4 = 11

algebra 1 solving equations

Answers

Answer: the variable is p=6 .

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

Answer:

p = 6

Step-by-step explanation:

Step 1: Simplify both sides.

3 + 2p − 4 = 11

3 + 2p + −4 = 11

(2p) + (3+−4) = 11 (Combine Like Terms)

2p + −1 = 11

2p − 1 = 11

Step 2: Add 1 to both sides.

2p − 1 + 1 = 11 + 1

2p = 12

Step 3: Divide both sides by 2.

2p/2 = 12/2

p=6

Other Questions
What is something about online conferencing that you understand better now. What did you learn? 7. How does the revolution of the Earth around the sun cause the seasons to change? please please please help which equation represents an exponential function that passes through the point (5,212.5) using form y=a(b)*x What is "the funniest thing" that happened after leaving Little Rock?AAlice Lovett started driving the car.BElden stopped calling Mrs. Gladstone.Mrs. Gladstone got stronger.DA caravan of stockholders followed the Cadillac to Texas. Fill in the blank with the French word that best completes the sentence.Je suis vgtarien. Je ne mange que (only) _____. O de la viande O des lgumesO du poissonO des fruits de mer Use the diagram below to answer the following question.Which of the following statements accurately describes the relative age of the fossils in these rock layers?A) The yellow shell fossils are from 300 million years agoB)The brown trilobite fossils are from 500 million years agoC)The brown trilobite fossils are older than the yellow shell fossilsD)The yellow shell fossils are older than the brown trilobite fossils I NEED HELP RN!! PLEASEAn oven is a technological system. Which of the following describes an input into this system? A. setting the temperature B. Burning gas releases heat. C. A thermostat monitors the temperature and increases the gas flow when the temperature falls too low. D. A cake is baked. your bank account is -$58.44. you deposit $46.85. what is your new balance? Someone help me please Where are the Galpagos Islands located? What are the jobs most commonly held by American workers, and which gender holds these jobs? Difference between essays and a passage describe how the amount of air changes as you travel up through earths atmosphere. Help me plz if i dont do this im in troble by my teacher. What does negative 5 over 2 < 1 indicate about the positions of negative 5 over 2 and 1 on the number line? (1 point)A. negative 5 over 2 is located on the left of 0 and 1 is located on the right of 0B. negative 5 over 2 is located on the right of 0 and 1 is located on the left of 0C. negative 5 over 2 is located on the left of 1D. negative 5 over 2 is located on the right of 1 There are 22 students, from which 6 people will be selected to be on a panel. If Allen and Joe are 2 of the 22 students, then what is the probability that neither will be selected to be on the panel?Round your answer to three decimal places. Why was this ordinance such a significant achievement? Your meal plan allows you 500 dollars to use per month. So far this month, you have used 345 dollars and you have 9 days left on this month's plan. Which inequality could you use to determine how many dollars at most you can use per day so that you don't go over your monthly plan dollars? Find the value of x for which r || s. Then find m Which of these grabs the readers attention and entices them to keep reading? the thesis statement the introduction the lead the subject