The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the football’s maximum height? Round to the nearest tenth. yds. How far is the football kicked? yds.

Answers

Answer 1

This is the equation of an upside down parabola, so the maximum height will be at the vertex. To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.
[tex]x=\frac{-1.53}{2*-.03}=25.5[/tex]

Plugging this into the given formula:
[tex]y=-0.03(25.5)^2+1.53(25.5)=19.5075[/tex]
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
[tex]0=-0.03x^2+1.53x=x(-0.03x+1.53)[/tex]

Then by the zero product property (or the no zero divisors rule), we have:
[tex]x=0[/tex] (this is the x value where the ball is kicked from)
[tex]-0.03x+1.53=0[/tex]
[tex]-0.03x=-1.53[/tex]
[tex]x=51[/tex]

So the ball travels 51 yards in total.

Answer 2

Answer:

Maximum height achieved by football = 25.5 yards.

Distance traveled by football 51 yards.

Step-by-step explanation:

Path of a football kicked by a field goal kicker can be modeled by the equation y = -0.03x² + 1.53x.

Where x represents horizontal distance and y represents height of the football.

For maximum, height we will find the [tex]\frac{dy}{dx}[/tex] ( derivative ) of the equation and equate it to zero.

[tex]\frac{d(y)}{dx}[/tex] = [tex]\frac{d}{dx}[/tex] (-0.03x² + 1.53x )

[tex]\frac{dy}{dx}[/tex] = -0.03 × 2x + 1.53

By putting [tex]\frac{dy}{dx}[/tex] = 0

-0.06x + 1.53 = 0

0.06x = 1.53

x = [tex]\frac{1.53}{0.06}[/tex] = 25.5 yards

Therefore, maximum height achieved by the ball is 25.5 yards.

Now for horizontal distance covered by ball y should be 0

-0.03x² + 1.53x = 0

x ( 1.53 - 0.03x ) = 0

0.03x = 1.53

x = [tex]\frac{1.53}{0.03}[/tex] = 51 yards.

Football was kicked 51 yards.

Related Questions

6a - 10 = 3a + 17 please explain how you got your answer

Answers

First we add 10 to both sides
next we add 3a + 17 + 10 so it can be 3a + 27
next we subtract 3a from both sides
next we subtract 6a - 3a and we get 3a
then we divide both sides by 3
and lastly we divide 27/3 to get our answer

Answer: a = 9.

Find two consecutive integers whose sum is 67.

Which of the following equations could be used to solve the problem?

2x = 67
2x + 1 = 67
2x + 2 = 67
x2 + 1= 67

Answers

Let the smaller integer be x.
The next larger consecutive integer is 1 more than x, so it's x + 1.

x + x + 1 = 67

2x + 1 = 67

Answer is option B.

Answer:

2x + 1 = 67

Let the smaller integer be x.

The next larger consecutive integer is 1 more than x, so it's x + 1.

x + x + 1 = 67

2x + 1 = 67

Which of these fractions can be written as a recurring decimal 1/2 1/3 1/4 1/5

Answers

1/3 can be written as 33.33333333333% as well as other forms so the answer is 1/3

The fraction that has a recurring decimal is 1/3 which turns in to 0.3333333333

Which function below has the smallest slope?

f(x)

f(x) = 2x − 3

g(x)

graph going through (0, negative 5) and (4, 3)
h(x)

x h(x)
−1 3
1 7
3 11
f(x)
g(x)
h(x)
The functions all have the same slope

Answers

Answer: The functions all have the same slope

Step-by-step explanation:

just took the assessment and I got it right.

HELP PLEASE ASAP!!!!!!!!!!!!!!!!!!!!

Answers

Line 4, you are supposed to divide/multiply before you add/subtract.

They added 5+16 but instead they should've divided 42/5.

Hope this was fast enough!

the mistake is in line 4 the correct answer is 24.4

y + 3 = –y + 9 solve

Answers

You need to isolate the variable.

y + 3 = -y + 9
Add y to both sides.
2y + 3 = 9
Subtract 3 from both sides.
2y = 6
Then divide 2 to solve for y.
y = 6
I hope this helps love! :)

Julie needs 3 lengths of string that are each 6 inches long. Marlene needs 7 lengths of string that are each 8 inches long.

How much string do the girls need altogether?

in.

Answers

seventy four because 6*3 is 18 and 7*8 is 56, add them to get 74

Tape diagram to subtract 33-19

Answers

well 33 - 19 = 14 and what do u mean tape diagram?

To subtract 19 from 33 using a tape diagram, draw a rectangle labeled 33, mark off a section labeled 19, and the unshaded difference represents the result, which is 14.

To create a tape diagram to show the subtraction of 33-19, we start by drawing a long rectangle to represent the number 33. We then mark off the length that represents the number 19 on the same tape, indicating the part we want to subtract. Lastly, the remaining part of the tape diagram represents the difference between the two numbers.

Draw a rectangle and label it 33.Mark a section of the rectangle and label it 19.Shade in or distinguish the remaining part of the rectangle; this is the result of 33 minus 19.See the unshaded part, which represents the difference, and count if necessary to find that it equals 14.

The final result is the length of the unshaded part of the tape diagram, which shows the difference when you subtract 19 from 33.

HOW many times can times 6 go into 59

Answers

6 can go into 59, nine times. Therefore 9 times 6 equals 54

All you have to do is divide 59/6, you get 9.83 hopefully this helps

For a craft project, two equilateral triangles are taped together to create a quadrilateral

Answers

The quadrilateral that is made is a rhombus. The triangle lines cause the quadrilateral to look like an uneven square or diamond which is also known as a rhombus.

If six plus two what does it equal

Answers

Six = 6

Two = 2

6 + 2 = 8

Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each weighed 12 lb more than the boxes Steven lifted.

Let s represent the weight of the boxes that Steven lifted.

Which expression represents the total number of pounds Nathan lifted?

s + 12

12(s+13)

15(s+12)

13(s+12)

Answers

13(s+12) is your answer
13 boxes that each weigh 12 more pounds than steven's boxes.

Answer:

13(s+12) is your answer

Step-by-step explanation:

What is the measure of an angle if the measure of its supplement is 39 degrees more than twice the measure of its complement?

Answers

angle is x. sup - adds up to 180. comp adds up to 90

180-x = 2(90-x)+39
180-x = 180-2x+39
180-x = 219-2x
180+x = 219
x = 39

Measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

What is angle?

" Angle is defined as when two rays meet at one endpoint known as vertex."

According to the question,

'x' represents the measure of an angle

Measure of its supplement angle = 180 - x

Measure of its complement angle= 90 - x

As per given condition of angle we get,

[tex]180 - x = 2(90 - x) +39\\\\\implies 180-x= 180 -2x +39\\\\\implies 2x-x = 39\\\\\implies x=39degrees[/tex]

Hence, measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

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Ruchi measured the area of her kitchen as

Answers

Ruchi measured the area of her kitchen as,

Answer:

She is incorrect because 2.81 × 10^4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches.

Terrance bought 3 markers. his sister bought 5 markers. terrance and his sister spent a total of $16 on the markers. what was the price of each marker?

Answers

each marker will cost $2

Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.

Answers

Hello Melissamv9321, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a2.

A total of 820 tickets were sold for the school play. they were either adult tickets or student tickets. there were 70 more student tickets sold than adult tickets. how many adult tickets were sold?

Answers

375 numbers of adult tickets were sold

By setting up a system of equations, we find that 375 adult tickets were sold for the school play.

To solve this problem, we need to set up a system of equations using the information provided:

There are only two types of tickets: adult tickets and student tickets.A total of 820 tickets were sold.There were 70 more student tickets sold than adult tickets.

Let's define the following variables:

A for the number of adult tickets.S for the number of student tickets.

According to the problem:

A + S = 820 (since the total number of tickets is 820)S = A + 70 (since there are 70 more student tickets than adult tickets)

Now we substitute the second equation into the first:

A + (A + 70) = 8202A + 70 = 8202A = 750A = 375

So, 375 adult tickets were sold.

Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answers

I can say that Jared and Nicole are correct because they manipulated the equation right. They can either write the equation as y as a function of x then substitute it to the y in the other equation and solve for x. They can also write the equation as x as a function of y and substitute it to x in the other equation and solve for y. For both solution, they will still obtain the same answers.

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.

Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

[tex]x=10y[/tex] and [tex]y-x=10[/tex].

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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Hot dogs cost $2.00 each, candy bars cost $1.00 each, and soft pretzels cost $2.50 each. How much would it cost to buy two hot dogs and one candy bar?

a. too much
b. too little

Answers

the answer for this question is too much

Final answer:

To calculate the total cost, multiply the price of each item by the number purchased then add those totals together. In this case, purchasing two hot dogs and one candy bar costs $5.00.

Explanation:

To find the total cost of purchasing two hot dogs and one candy bar, you would simply multiply the cost of each item by the number of that item you are buying, and then add all these costs together. So, if a hot dog is $2.00 and you want to buy two, this costs $2.00 * 2 = $4.00. A candy bar is $1.00 each, and if you want to buy one, this costs $1.00 * 1 = $1.00. So, the total cost would be the cost of the hot dogs plus the cost of the candy bar, which is $4.00 + $1.00 = $5.00. Therefore, the total cost of two hot dogs and one candy bar is $5.00.

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The diameter of the circle above is 94 cm. what is the circumference of the circle? (use = 3.14.)

Answers

To find the circumference, you multiply the diameter by pi (3.14).

94 * 3.14 = 295.16

Hope this helps!

A histogram can help you make predictions about a set of data. True False

Answers

This is true because a histogram lets you discover and show the underlying frequency distribution

The sum of two numbers is 35 . the smaller number is 19 less than the larger number. what are the numbers?

Answers

let the smaller number be x and the larger be (x+19)
x+x+19=35
2x=16
x=8
x+19=27

the numbers are 8 and 27.

Help please
Solve for r.

s=2πrh

Answers

s/2πh=r

hope this helps u

Here it is
I hope that will help you

Mark the statements that are true.

A. An angle that measures is a reflex angle.
B. An angle that measures 65 is an acute angle.
C. An acute angle measures less than .
D. An angle that measures 300 is an obtuse angle.

Answers

The correct options are B. An angle that measures 65 is an acute angle. and C. An acute angle measures less than 90 degrees.

To determine the truth of each statement, let's analyze each option:

A. An angle that measures 180 degrees is a reflex angle.

This statement is false. An angle that measures exactly 180 degrees is a straight angle, not a reflex angle. A reflex angle is greater than 180 degrees but less than 360 degrees.

B. An angle that measures 65 degrees is an acute angle.

This statement is true. An acute angle is an angle that measures less than 90 degrees. Since 65 degrees is less than 90 degrees, it is indeed an acute angle.

C. An acute angle measures less than 90 degrees.

This statement is true. By definition, an acute angle is any angle whose measure is less than 90 degrees.

D. An angle that measures 300 degrees is an obtuse angle.

This statement is false. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Since 300 degrees is greater than 180 degrees, it is not an obtuse angle but rather a reflex angle.

Solve 12g=12(2/3g-1)+11

Answers

Solve for g:12 g = 12 ((2 g)/3 - 1) + 11
Put each term in (2 g)/3 - 1 over the common denominator 3: (2 g)/3 - 1 = (2 g)/3 - (3)/3:12 g = 12 (2 g)/3 - (3)/3 + 11
(2 g)/3 - (3)/3 = (2 g - 3)/3:12 g = 12 (2 g - 3)/3 + 11
12/3 = (3×4)/3 = 4:12 g = 4 (2 g - 3) + 11
4 (2 g - 3) = 8 g - 12:12 g = 8 g - 12 + 11
Grouping like terms, 8 g - 12 + 11 = 8 g + (11 - 12):12 g = 8 g + (11 - 12)
11 - 12 = -1:12 g = 8 g + -1
Subtract 8 g from both sides:12 g - 8 g = (8 g - 8 g) - 1
12 g - 8 g = 4 g:4 g = (8 g - 8 g) - 1
8 g - 8 g = 0:4 g = -1
Divide both sides of 4 g = -1 by 4:(4 g)/4 = (-1)/4
4/4 = 1:Answer: g = (-1)/4

He length of a rectangle is six times its width. if the perimeter of the rectangle is 70 in , find its area.

Answers

The width is 150 inches squared

For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine

Answers

The vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
___________________________________________
Explanation:
___________________________________________

f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

We know that "(x² − 9) ≠ 0 ; since we cannot divide by "0" ; so the "denominator" in the fraction cannot be "0" ;

since: 9 − 9 = 0 ; "x² " cannot equal 9.

So, what values for "x" exist when "x = 9" ?

x² = 9 ;

Take the square root of EACH SIDE of the equation ; to isolate "x" on one side of the equation ; and to solve for "x" ;

√(x²) = √9 ;

x = ± 3
__________________________________________
So; the vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
__________________________________________
(since: We have: f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

The "x² / x² " as the highest degree polymonials; both with "implied" coefficients of "1" ; and both raised to the same exponential power of "2".

HELP URGENT NEED TO PASS :(((((

Answers

It goes through (4,0) and (0,-4) so by slope formula, (4-0)/(0--4)=4/4=1

Slope is rise divided by run, or rise over run.
Look at a point on the graph, for example, (0, -4).
How much do you need to go up and then right to get to the next point?
If you go up 1 and right 1, you get to point (1, -3) which is also on the graph.
Going up 1 is a rise of 1.
Going right 1 is a run of 1.
Slope = rise/run = 1/1 = 1

If chungs go kart can travel 48 miles on 1 gallon of gas,how far can his go kart travel with 1.15 gallons of gas?

Answers

your answer is 55.2
you take 1.15 times 48
i hoped i helped

He can travel 55.2 miles with 1.15 gallons of gas on his go-kart.

Set up a proportion. 1 over 48 is equal to 1.15 over x. Use cross products multiply 48 by 1.15 to get 55.2 and divide that by 1 to get 55.2.

x=55.2 miles.

Hope this helps!
Can u plz mark me as brainliest? I really need it!

Eli needs to save $235. to earn money, he plans to mow lawns and charge $21 for each, write two estimates eli could use to determine the number of lawns he needs to mow. decide which estimate you think is the better one for eli to use

Answers

To determine the number of lawns he needs to mow to earn the desired money, Eli could perform a simple addition problem, adding $21 per lawn until he reached his goal number. This equation would be: 21 + 21 = 42 + 21 = 63 + 21 = 84 + 21 = 105 + 21 = 126 + 21 = 147 + 21 = 168 + 21 = 189 + 21 = 210 + 21 = 231 + 21 = 252. However, a better way would be to divide the desired amount by the cost per lawn and round to the nearest whole number. That equation is 235 / 21 = 12 lawns.

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