A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.
Write an equation to model the height h in feet of the ball t seconds after it has been punted.
The football is caught at 5.5 feet above the ground. How long was the football in the air?

Answers

Answer 1

The standard kinematics equation is for an object projected vertically is:
H(t)=H0+v0(t)+(1/2)at^2
H0=height at time 0
v0(t)=vertical velocity at time 0
a=acceleration [equals -g for gravity]
H(t) height of projectile at time t.

We're given
H0=2.5'
v0=45 '/s
a=-32.2 '/s^2

so the kinematics equation is
H(t)=2.5+45(t)+(1/2)(-32.2)t^2= 2.5+45t-16.1t^2

Solve for H(t)=5.5 using the quadratic formula:
H(t)=5.5= 2.5+45t-16.1t^2
t=0.0683 s [ on its way up ], or
t=2.727 s [caught on its way down]

Therefore the football was in the air for 2.727 seconds.

Related Questions

py+7=6y+q
what is the answer for this question (linear equations with unknown coefficients)?

Answers

Assuming your solving for y:
py+7=6y+q
-6y -7 -6y -7
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)

Answer:

The required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]py+7=6y+q[/tex]

We need to simplify the equation and convert it into a linear equation with unknown coefficients.

Subtract 6y from both sides.

[tex]py - 6y + 7 = q[/tex]

Subtract 7 from both sides.

[tex]py - 6y = q - 7[/tex]

Take y common from left side.

[tex]y(p-6) = q-7[/tex]

Divide both sides by p-6.

[tex]y =\frac{(q-7)}{(p-6)}[/tex]

Hence, the required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].

solve for y 6y-8=3y-2

Answers

6y-8 =3y-2

subtract 3y from both sides

3y-8 = -2

add 8 to both sides

3y=6

y=6/3 =2

y = 2

What is the solution to the equation 0.8m − 4 = −0.8m?

Answers

m= 2.5 that's the solution for m for them to be equal

0.8m − 4 = −0.8m
0.8m + 0.8m = 4
1.6m = 4
m = 4 /1.6
m = 2.5

what is the area of a circle with a radius of 7 inches

Answers

Area formula is A=πr2
A=3.1416(radius)2 (radius is 7)
A=3.1416(49)
A=153.94
The area is 153.94 inches.
Hope that was helpful :)

Answer is provided in the image attached.

Question help a robotic rover on mars finds a spherical rock with a diameter of 1313 centimeters. the rover picks up the rock and lifts it 1515 centimeters straight up. the rock has a specific gravity of 5.255.25. the gravitational acceleration on mars is 3.73.7 meters per second squared. if the robot's lifting arm has an efficiency of 3535% and required 1212 seconds to raise the rock 1515 centimeters, how much power (in watts) did the arm use?

Answers

Due to apparent doubling of numbers in the question, assume
diameter=13 cm/2=0.065m
h=15 cm=0.15m
rho=5.25*1000=5250 kg/m^3
eta=35%=0.35 [efficiency]
t=12 s
g=3.7 m/s^2

mass, m=rho*V=rho*(4pi/3)(r^3)
=5250 kg/m^3 * (4pi/3)(0.065)^3 m^3
=1.922 kg

Work done in lifting h=0.15m
W=mgh
=1.922pi kg * 3.7 m/s^2 * 0.15 m
=1.067pi kg (m/s)^2
=1.067pi J

Average power required, with efficiency eta=0.35
P=(W/t)/eta
=(1.067pi J )/ (12 s) /0.35
=0.254pi J/s
=0.798W (approx.)

PLEASE HELP !!! HURRY!! Given m || n, find x.

Answers

4x+35 + 5x-8 = 180

9x +27 =180

9x =153

x=153/9 = 17

x = 17

The answer is x=9x+27

Describe the relationship between the similarity ratio of two triangles and the ratio of their areas.

Answers

[tex]\bf \textit{let's say the sides ratio is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{s_1}{s_2} \\\\\\ \textit{then the ratio of their areas is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{(s_1)^2}{(s_2)^2}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}[/tex]

help find the answer to this question

Answers

First, find the area of the entire traingle using the formula bh/2.
18*9/2=81 cm^2
Then subtract the area of the smaller triangle within the larger one (white triangle). It has the same base but a height of only 4.
18*4/2=36 cm^2
81-36=45
Final answer: 45 cm^2

The circumference of a circle is 6.28. What is the area of the circle.

Answers

Hello there! Thank you for asking your question here at Brainly. I will be assisting you today with how to handle this problem, and will teach you how to handle it on your own in the future.

First, let's evaluate the question.
"The circumference of a circle is 6.28. What is the area of a circle?"

Now, let's remember the different formulas for area and circumference.
The circumference is "2•3.14•r", while the area is "3.14•r•r".

We have our circumference, 6.28.
However, we are looking for the area. Since we have the circumference, we need to narrow down to the radius (so we can solve for the area).
Let's set this up as an equation;
C = 2 • 3.14 • r
Plug in the value for our circumference.
6.28 = 2 • 3.14 • r
Multiply 2 by 3.14 and r to simplify the right side of the equation.
2 • 3.14 • r = 6.28 • r = 6.28r

We're now left with:
6.28 = 6.28r
Divide both sides by 6.28 to solve for r.
6.28 / 6.28 = 1
6.28r / 6.28 = r

We are now left with the radius:
R = 1.

Now, we can solve for the area.
Remember our formula for the area.
A = r • r • 3.14.
Plug in 1 for r.
A = 1 • 1 • 3.14
A = 3.14.

Your area is 3.14 units^2.

I hope this helps, and has prepared you for your future problems in relation to this topic!

Circumfrence= πd
6.28=3.14*d
6.28/3.14=d
D=2
Area= πr*r
=3.14*1*1
=3.14

A pizza parlor sold 38 1/8 pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?

Answers

38*8 = 304

304 + 1 =305 slices were sold

8(38 1/8)

8(38)+8(1/8)

304+1

305 slices.

A sofa is on sale for 26% off. The sale price is $629 . What is the regular price?

Answers

100% - 26% = 74%

74% ..............$629
100% ..............?

629 x 100/74 = 850

answer
regular price is $850

The regular price is $850 hope this helped

Help Please question in the file.

Answers

check the picture below.

today there are 3,659 thousand elementary and secondary teachers employed in a certain country. this number is expected to increase to 3,856 thousand by next decade. what is the percent increase?

Answers

percent increase = (new number - original number) / original number...* 100
= (3856 - 3659) / 3659...* 100
= 197 / 3659....* 100
= 0.0538 * 100
= 5.38% <==

In a certain company, 74 employees were hired in the last 5 years. If
this represents 43% of the current number of employees, then how
many current employees does the company have?

- list the steps please & thank you!

Answers

You have to be able to take the written words and turn them into a workable equation. 74 employees is 43% of the current number, which you don't know. The word "is" means = , the 43% is written as .43, the word "of" means to multiply and the current number of employees, what you're looking for, is your unknown x. So translating those words into an equation looks like this:
74 = .43x. And dividing both sides by .43 you get that the current number of employees is 172.09, or just 172

Final answer:

To find the total number of employees in the company, set up and solve the equation, 0.43 * X = 74. Solving this provides approximately 172 employees

Explanation:

In order to answer this question, we need to use the concept of percentages. Here are the steps:

Since we know 74 employees represent 43% of all employees, we set up the equation: 0.43 * X = 74, where X is the total number of employees in the company. Solving the equation for X leads us to the answer. We divide both sides of the equation by 0.43, which gives us X = 74/0.43. Calculating the right side of the equation, we find X is approximately 172, so there are approximately 172 employees in the company.

Learn more about Percentages here:

https://brainly.com/question/29306119

#SPJ12

Suppose that an individual has a body fat percentage of 17.9% and weighs 132 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.

Answers

f=132(17.9/100)

f=2362.8/100

f=23.628

f≈23.6 pounds (to nearest tenth of a pound)

Breanna works in the mall and her hours increase during busy shopping times of the year. Breanna has a plan to save $25 each week for 5 weeks, and then increase that amount by $20 for the next 7 weeks during the busy time, then go back to $25 per week. If Breanna’s plan is to save $540, how many weeks total will she need to save?
a.
11 weeks
b.
16 weeks
c.
22 weeks
d.
23 weeks

Answers

The math I used is probably not the quickest way, but for me, the easiest.
25*5=125 25+20=45 45*7=315 125+315=440 25*4=100 440+100=540 5+7+4=16
B is your answer.

Answer:

Number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

Step-by-step explanation:

As given

Breanna works in the mall and her hours increase during busy shopping times of the year.

Breanna has a plan to save $25 each week for 5 weeks.

Thus

Breanna saves in first 5 weeks = Amount saves per weeks in next 5 weeks × Number of weeks .

= $25 × 5

= $ 125

Increase that amount by $20 for the next 7 weeks during the busy time.

Thus

Amount saves per weeks for next 7 weeks = Amount saves per weeks in first 5 weeks + Increase in amount .

= $25 +$ 20

= $ 45

Breanna saves in next 7 weeks = Amount saves per week× Number of weeks .

Put all the values in the above

= $45 × 7

= $ 315

As given

Breanna saves $25 per week.

If Breanna’s plan is to save $540 .

Let us assume last weeks in which Breanna saves $25 per weeks be x .

Breanna saves in last x weeks = Amount saves for next x weeks × Number of weeks .

= 25 × x

= 25x

Equation becomes

Breanna saves in first 5 weeks + Breanna saves in next 7 weeks + Breanna saves in last x weeks = Total saving amount .

125 + 315 + 25x = 540

440 + 25x = 540

25x = 540 - 440

25x = 100

[tex]x = \frac{100}{25}[/tex]

x = 4 weeks

Thus

Total number of weeks Breanna saves = 5 weeks + 7 weeks + 4 weeks

= 16 weeks

Therefore the number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

simplify the expression by using a double angle formula

cos^2 4theta-sin^2 4theta

Answers

Double angle formula for cos(2x) is
cos(2x)=cos^2(x)-sin^2(x)

Substitute x=4theta, then
cos(8theta)=cos^2(4theta)-sin^2(4theta)
=>
cos^2(4theta)-sin^2(4theta) = cos(8theta)

Find the value of x
A 41
B 44
C 46
D 36

Answers

This time it's cosine.

Cosine is the adjacent/hypotenuse. In this case, the adjacent is 15 and hypotenuse is 21.

15/21, or like 5/7.

Now put that into a fancy calculator with the [tex]cos^{-1} [/tex] thing or something like that and then you have the answer, or around 44 degrees.

The radius of the circle whose equation is (x + 4)² + (y - 2)² = 36 is 36 18 6

Answers

[tex]36=r^2\\r=6[/tex]

The equation of a circles is:

(x-h)^2+(y-k)^2+r^2, where (h,k) is the center of the circle and r is the radius

r^2=36

r=√36

r=6

palace help me solve these two equations 14, 15

Answers

14)

check the picture below... so.. is just a semi-circle and a rectangle, nothing fancy, get their area, sum them up.

15)

so... the voter turnout, is referring to, what's the percentage that voted, which year has the highest percentage... well, we simply check the percentage of the value provided from the total eligible voters, keeping in mind that, all eligible voters are the 100%

so.. for 1944

[tex]\bf \begin{array}{ccllll} amount&\%\\ ------&----\\ 86,607,000&100\\ 47,976,670&x\\ \end{array}\implies \cfrac{86,607,000}{47,976,670}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 47,976,670}{86,607,000}\implies x\approx 55.39583405498[/tex]

for 1984

[tex]\bf \begin{array}{ccllll} amount&\%\\ -----&-----\\ 167,727,000&100\\ 92,659,000&x \end{array}\implies \cfrac{167,727,000}{92,659,000}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 92,659,000}{167,727,000}\implies x\approx 55.2439380660239[/tex]

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. (remember, m is a factor of n if m divides n evenly.)

Answers

This is the following condition in order to get the specific output for this specific problem: if is_a_prime(n): is_prime = True Now all you have to do is write is_a_prime().

For the hard code for this problem:

if n == 2:
is_prime = True
elif n % 2 == 0:
is_prime = False
else:
is_prime = True
for m in range (3, int (n * 0.5) + 1, 2):
if n % m == 0:
is_prime = False
break.

To add, a high-level programming language that is widely used for general-purpose programming, created by Guido van Rossum and first released in 1991 is called Python.

Below is the solution of assign true to is_prime if n has no factors other than 1 and itself.

Further explanation

Python is an interpreted, high-level, general-purpose programming language. Python is created by Guido van Rossum and first released in 1991. Its design philosophy emphasizes code readability. Python is a more productive language than Java because it is an interpretive language which is accompanied by elegant syntax and it makes an excellent choice for scripting and rapid application development in many areas. Python is a general-purpose, versatile and popular because it is concise and easy to read, and it is also a good language to have in any programmer’s stack as it can be used for everything such as web development, software development, data science applications.

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. And remember, m is a factor of n if m divides n evenly. So:

if n == 2:

is_prime = True

elif n % 2 == 0:

is_prime = False

else:

is_prime = True

for m in range (3, int(n**0.5)+1, 2):

if n % m == 0:

is_prime = False

Learn moreLearn more about python https://brainly.com/question/4331067Learn more about python IDLE or similar environment https://brainly.com/question/6280029Learn more about python function https://brainly.com/question/9806744

Answer details

Grade: 9

Subject: mathematics

Chapter: python

Keywords: python, integer, factors, python IDLE, is_prime

D=6.3cm what is the circumference and area of the circle

Answers

Circumference = 2pir
=2×pi×1.6
=10.05

Area= pir^d
=pi × 6.3
=19.79

Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018? a. 70% b. -27% c. -17% d. -75%

Answers

Using linear function concepts, it is found that the industry’s percent change from 2008 to 2018 will be of:

b. -27%

What is a linear function?

A linear function is modeled by:

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

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.

In this problem:

The industry had 63.1 thousand jobs in 2008, hence b = 63.1.This number is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018, hence m = -1.7.

Thus, the function is:

y = -1.7x + 63.1.

In 2018, which is 10 years after 2008, the value of the function is:

y(10) = -1.7(10) + 63.1 = 46.1.

The percent change is given by the change divided by the initial value, hence:

(46.1 - 63.1)/63.1 = -27%

Hence option b is correct.

More can be learned about linear function concepts at https://brainly.com/question/24808124

The correct answer is b. -27%.

To solve this problem, we need to find the number of jobs in 2018 and then calculate the percent change from 2008 to 2018.

Given information:

- Number of jobs in 2008: 63.1 thousand

- Average annual rate of decline: 1.7 thousand jobs per year

- Time period: 2008 to 2018 (10 years)

Step 1: Find the total decline in jobs from 2008 to 2018.

Total decline in jobs = Average annual rate of decline × Number of years

Total decline in jobs = 1.7 thousand × 10 years = 17 thousand jobs

Step 2: Find the number of jobs in 2018.

Number of jobs in 2018 = Number of jobs in 2008 - Total decline in jobs

Number of jobs in 2018 = 63.1 thousand - 17 thousand = 46.1 thousand jobs

Step 3: Calculate the percent change from 2008 to 2018.

Percent change = (Change in value / Original value) × 100%

Percent change = ((46.1 - 63.1) / 63.1) × 100%

Percent change = (-17 / 63.1) × 100%

Percent change ≈ -27%

Therefore, the industry's percent change from 2008 to 2018 is approximately -27%.

Number of jobs in 2018 = [tex]46.1\text{ thousand} \\[/tex]

Percent change from 2008 to 2018 = [tex]-27\%[/tex]

The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test? Show your work. A. List the two equations B. Find each type of question

Answers

x is 2 pt questions
y is 4 pt questions
x+y=34
2x+4y=80
Multiply the top equation by -2 to use elimination technique
-2x-2y=-68
Then combine the two equations (x is cancelled out)
2y=12
y=6
If there are 6 four point questions, there must be 28 two point questions to get a total of 34 questions.

Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. How many spare tires of this same variety must carried so that a trip of 15,000 miles can just be completed.

Answers

3 spare tires are needed. This works if you rotate the tires every 5,000 miles.

Tire A, B, C, D (and spare is E F G)
first 5,000 miles you use tire A B C D
second 5000 miles you use tire B C D E
third 5000 miles you use A E F G

Each tires is used no more than twice (10,000 miles).

One weekend, a newsstand sold twice as many Sunday papers as Friday papers. The Sunday paper costs $1.50, and the Friday paper costs $0.75. How many Sunday papers were sold if the newsstand took in $116.25?

Answers

1.50s + 0.75f = 116.25
2f = s

1.50(2f) + 0.75f = 116.25
3f + 0.75f = 116.25
3.75f = 116.25
f = 116.25/3.75
f = 31...31 friday papers

2f = s
2(31) = s
62 = s <=== 62 sunday papers

Answer:

Step-by-step explanation:

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)

Answers

part A)

[tex]\bf \begin{array}{ccllll} hours(x)&velocity(y)\\ -----&-----\\ 2&50\\ 6&54 \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 50}})\quad % (c,d) &({{ 6}}\quad ,&{{ 54}}) \end{array}[/tex]

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{54-50}{6-2}\implies \cfrac{4}{4}\implies 1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-50=1(x-2)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-50=x-2\implies \boxed{y-x=48}\impliedby \begin{array}{llll} standard\\ form \end{array}[/tex]

part B)

well, to graph a LINEar equation, since it's just a LINE, you simply need two points to graph a line, and since we know that y - x = 48.... if you want to know what's "y" when x = 7? or 7 hours, well

y - (7) = 48
y = 48 + 7
y = 55

so.. that's the point for the 7th hour, 7, 55, and you can pick any other point above, and graph it away.

If 2m = 4x and 2w = 8x, what is m in terms of w?

Answers

2^m=2^n take the natural log of both sides

m*ln2=n*ln2 divide both sides by ln2

m=n

you can simply divide the eqution or you substitute the value of x in any equation.

What is the future value of $845 a year for seven years at an interest rate of 11.3 percent? $6,683.95 $6,075.69 $8,343.51 $8,001.38 $8,801.91?

Answers

the future value of cash whose initial value is $845, at the rate of 11.3% for 7 years will be calculated using the compound interest rate, that is:
A=p(1+r/100)^n
where:
A=future amount
r=rate=11.3%=0.113
time=7 years
thus the future value of our cash will be:
A=845(1+0.113)^7
A=845(1.113)^7
A=$1,787.82

In 7 years, you will have $1,787.82

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.

Answers

Let a_0 = 100, the first payment. Every subsequent payment is the prior payment, times 1.1. In order to represent that, let a_n be the term in question. The term before it is a_n-1. So a_n = 1.1 * a_n-1. This means that a_19 = 1.1*a_18, a_18 = 1.1*a_17, etc. To find the sum of your first 20 payments, this sum is equal to a_0+a_1+a_2+...+a_19. a_1 = 1.1*a_0, so a_2 = 1.1*(1.1*a_0) = (1.1)^2 * a_0, a_3 = 1.1*a_2 = (1.1)^3*a_3, and so on. So the sum can be reduced to S = a_0 * (1+ 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) which is approximately $5727.50

Other Questions

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