During halftime of a football game a slingshot launches T-shirts at the crowd a T-shirt is launched from a height of 6 feet with an initial upward velocity of 72 ft./s the T-shirt is cot 45 feet above the field how long will it take the T-shirt to reach the maximum height what is the maximum height what is the range of the function that models the height of the T-shirt overtime

Answers

Answer 1

Answer:

2.25 seconds

87 feet

[6, 87]

Step-by-step explanation:

The height of a projectile is:

h(t) = -16t² + vt + s

where v is the initial vertical velocity and s is the initial height.

Here, v = 72 and s = 6.

h(t) = -16t² + 72t + 6

This is a downwards parabola.  The maximum is at the vertex.

t = -b / (2a)

t = -72 / (2×-16)

t = 2.25

h(2.25) = 87

It takes 2.25 seconds to reach the maximum height of 87 feet.

The range is from the lowest height (6 feet) to the maximum height (87 feet).  In interval notation:

[6, 87]

Answer 2

Final answer:

This response explains the time to reach maximum height, calculates the maximum height, and determines the range function for the projectile motion of the T-shirt launched by a slingshot during halftime at a football game.

Explanation:

Maximum Height Calculation:

Find the time taken to reach the maximum height using the formula: t = V₀/g, where V₀ is the initial velocity and g is the acceleration due to gravity.Substitute the values: t = 72 ft./s / 32 ft./s² = 2.25 seconds.Calculate the maximum height using the formula: H = V₀t - 0.5gt².Substitute the values: H = 72 ft./s x 2.25 s - 0.5 x 32 ft./s² x (2.25 s)² = 81 feet.

Time to Reach Maximum Height: 2.25 seconds

Maximum Height: 81 feet

Range Function: The range function (horizontal distance) can be determined using the formula: R = V₀t, where V₀ is the initial velocity and t is the time taken to reach the maximum height.


Related Questions

3 3/5 divided by 2 1/4 in simplest form

Answers

(3+3/5) ÷ (2+1/4) = 1.6

Answer:

Exact form: 8/5

What are all the factors of 2x^2-6x

Answers

Answer:

2x (x-3)

Step-by-step explanation:

Answer:

2x(x - 3).

Step-by-step explanation:

2x is common so if we divide 2x^2 - 6x by 2x we get x - 3 and the factors are:

2x(x - 3).

Please help. I dont know what Im doing!

Answers

The Fendley family is planning a vacation, and they are trying to choose which resort they will stay in. Mrs. Fendley has created the table below showing their four options. They want to spend no more than $250 per night for the resort. Which resorts will fit into their budget? Select two that apply.

Resort Amount Charged

A $550 for 2 nights

B $694 for 3 nights

C $1028 for 4 nights

D $1153 for 5 nights

A no

Resort A $275 per night

B maybe

Resort B $231.33 per night

C no

Resort C $257 per night

D maybe

Resort D $230.60 per night

the answer is b or d you choose which one you would like to choose

In the xy coordinate plane the slope of line p is 1 2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept. A) y = -2x - 3 B) y = -2x + 3 C) y = -2x - 6 D) y = -2x + 6

Answers

Answer:

Option C) y = -2x - 6

Step-by-step explanation:

The correct question is

In the xy coordinate plane the slope of line p is 1/2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept.

step 1

Find the slope of a line that is perpendicular to p

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=\frac{1}{2}[/tex] ----> slope of line p

substitute

[tex](\frac{1}{2})*m_2=-1[/tex]

[tex]m_2=-2[/tex] ----> slope of the line perpendicular to p

step 2

Find the equation of the line  that is perpendicular to p and intersects p at is x-intercept

we have

[tex]m=-2[/tex]

[tex]point\ (-3,0)[/tex]

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-0=-2(x+3)[/tex]

[tex]y=-2x-6[/tex]

how many solutions does 6x-6=6x+15 have

Answers

Answer:

None

Step-by-step explanation:

Note that we have 6x on both sides here.  If we subtract 6x from both sides, the equation becomes -6 = +15, which is never true.

Thus, this equation has NO SOLUTION.

Jim went to a carnival with $25.00. He bought some food for $3.75. Jim wants to spend the rest of his money on tickets for rides, r, which cost $1.25 each. Which represents, r, the number of tickets Jim can purchase?
(A) r less than equal 17
(B) r greater than equal 17
(C) r less than equal 20
(D) r greater than equal 20

Answers

Answer:

A

Step-by-step explanation:

25.00-3.75 is 21.25. divide that by 1.25 to get exactly 17.

Answer:A

Step-by-step explanation:

what fraction is equal to .13

Answers

Answer: 13/100

Step-by-step explanation:

any number with 100 as it denominator and that is less than 100 is it's self but move the decimal back for how many place values it have.

for example:

1/100=  .1

99/100= .99

The decimal 0.13 is equivalent to the fraction 13/100, as the number has two decimal places, and the fraction's denominator is set to 100.

The decimal 0.13 can be expressed as a fraction where the denominator is a power of 10 equivalent to the number of decimal places. To convert 0.13 to a fraction, you consider that there are two decimal places, so you use 100 as the denominator. Therefore, 0.13 as a fraction is 13 over 100, which can be written as 13/100.

This is because to convert a decimal to a fraction, you write down the numbers to the right of the decimal point as the numerator and a power of 10 that corresponds to the number of decimal places as the denominator. In the case of 0.13, since there are two decimal places, the power of 10 used is 102, which is 100.

Please help :DDDDDD
question is in the pic!

Answers

Equivalent expressions to given expression are:

A : -8+19-3x

C : -11x+19

Step-by-step explanation:

Given

[tex]-5+4(-2x+6)-3x[/tex]

We will simplify the given expression to find the equivalent expressions

[tex]-5+4(-2x+6)-3x\\= -5-8x+24-3x\\= -8x+19-3x\\=-11x+19[/tex]

by observing the simplification we can see that the equivalent expressions are:

A : -8+19-3x

C : -11x+19

Keywords: Polynomials, Expressions

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What slope passes through -3,7 and is parallel to 4x-1?

Answers

Answer:

y = 4x + 19

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\ k:y=4x-1\to m_1=4.\\\\\text{Therefore}\ m_2=4.\\\\l:y=4x+b\\\\\text{Put the coordinates of the point (-3, 7) to the equation of a line:}\\\\7=4(-3)+b\\7=-12+b\qquad\text{add 12 to both sides}\\19=b\to b=19\\\\\text{Finally:}\\\\y=4x+19[/tex]

Is the sequence -3, 1, 5, 9,... An arithmetic sequence

Answers

Answer:

Yes, it's an arithmetic sequence.

Step-by-step explanation:

Each term in this sequence is 4 more than the previous term.  Therefore we have an arithmetic sequence.

You can rent time on computers at the local copy center for a a ​$ 7 setup charge and an additional ​$ 3.50 for every 10 minutes. How much time can be rented for ​$ 22?

Answers

Answer:

The answer should round up to 40 minutes. Do it to make sure the answer is 4 which in this case = 40

Step-by-step explanation:

[tex]22 - 7 \div 3.50[/tex]

Answer:

Computer can be rented for  42.85 minutes using $22

Step-by-step explanation:

Given:

Setup charge =  ​$ 7

Additional charge for every 10 minutes = ​$ 3.50

To find:

The time for which the computer can be rented for  ​$ 22

Solution:

Let the additional time be x

for  additional charge for 10 minutes =3.50

for 1 minute , additional charge = [tex]\frac{3.50}{10}[/tex]= $0.35

According to the question

setup cahrge + additional charge= $22

[tex]7+(0.35\times x)=22[/tex]

[tex](0.35\times x)=22-7[/tex]

[tex](0.35\times x)=15[/tex]

[tex]x=\frac{15}{035}[/tex]

x=42.85


What is the value of x?
3
4
6
8 ​

Answers

Answer:

4

Step-by-step explanation:

Gave a picture to explain

Answer: I can confirm x=4

Step-by-step explanation:

-10x+9x=12 solve for x equation

Answers

Answer:

x = -12

Step-by-step explanation:

Remember that ax + bx = (a+b)x

-10x + 9x = 12

Add -10x and 9x together

(-10 + 9)x = 12

-x = 12  (-1x is written as -x, just as 1x is written as x)

÷ -1 both sides

x = -12

I hope this helps. Happy studying. :)

-10x+9x= -1x

-1x=12 -1 divided by 12 equals -12 Therefore x = -12

What is 34 to 35 reduce in its simplest form of numbers

Answers

Answer:

34/35=0.9714285

Step-by-step explanation:

Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue. What fraction of Megan’s star sticker are blue?

Answers

Answer:

The fraction of Megan's blue stickers are 1/6.

Step-by-step explanation:

Given:

Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue.

Now, to find the fraction of stickers which are blue.

Total number of stickers  =  12.

Number of red stickers are = [tex]12\times \frac{1}{2}[/tex]

                                              = [tex]6 stickers[/tex]

Number of green stickers are = [tex]12\times \frac{1}{3}[/tex]

                                                  = [tex]4 stickers[/tex]    

Number of blue stickers are = [tex]12-(6+4)[/tex]

                                               = [tex]12-10=2 stickers[/tex]

Now, to get the fraction of stickers we divide the number of blue stickers by the total number of stickers:

Fraction of blue stickers = [tex]2\div 12[/tex]

                                         = [tex]\frac{1}{6}[/tex]

Therefore, the fraction of Megan's blue stickers are 1/6.

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The table below shows the amount g(r), in dollars, after r years

r(number in years) 1///2
g(r) (amount in dollars)9,638///18,794.10

what was the percent change from year 1 to year 2?

Answers

Answer:

48.72%

Step-by-step explanation:

(18794.10-9638)/18794.10*100 = 9156.1/18794.10*100 = 48.72%

12x + 3y = 15 for x = -1,0,1

Answers

The chosen topic is not meant for use with this type of problem. Try the examples below.
x−y=9,x+y=6
x+y=4,x-y=2
x+y=3,2x-8y=19

consider the parabola with a focus at the point (0,-3) and directrix y=2 . which two equations can be used to correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola ?

Answers

Final answer:

The two equations that can be used to relate the distance from the focus and the directrix to any point on the parabola are x² = 4py and y = (x-k)² + h.

Explanation:

To correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola, we can use the following two equations:

x² = 4pyy = (x-k)² + h

Where p is the distance from the focus to the directrix, (h,k) is the vertex of the parabola, and the equation x² = 4py represents a parabola with its axis parallel to the y-axis, and y = (x-k)² + h represents a parabola with its axis parallel to the x-axis.

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3. In a single growing season at the Smith Family Orchard, the average yield per apple
tree is 150 apples when the number of trees per acre is 100. For each additional tree
over 100, the average yield per tree decreases by 1.
a. What would be the average yield per tree if the number of trees per acre was
doubled? What would be the total yield in that case?
b. How many trees should be planted per acre to maximize the total yield?

Answers

Answer:

a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.

b. 25 more trees are to be planted per acre to maximize the total yield.

Step-by-step explanation:

If the no. of trees per acre is doubled then it will be equal to,

[tex]100 \times 2[/tex]

= 200

So, the no. of trees per acre is increased by (200 - 100) = 100

hence, the average yield per tree will be,

(150 - 100) = 50 in that case.

Hence, the total yield will be,

[tex]50 \times 200[/tex]

= 10,000 apples per acre

Now , if x trees are planted, the total no. of apples produced per acre will be,

[tex](150 - x) \times (100 + x)[/tex]

= [tex]15000 + 50x - x^{2}[/tex]

= f(x) [say]

So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)

= 50 - 2x---(1)

taking f'(x) = 0 , we get,

50 - 2x = 0

⇒ x = 25 --------------(2)

Again,

[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25

=  -2 (<0)

So, f(x) attains it's maximum value at x = 25

Hence,

25 more trees are to be planted per acre to maximize the total yield.

Three points of a function are graphed.

A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
Which statement describes the function through the points?

The function is a direct variation function with a constant of variation of 1.5.
The function is a direct variation function with a constant of variation of 1.8.
The function is linear but is not a direct variation function.
The function is not a linear function.

Answers

Final answer:

The function through the points (10, 18), (14, 24), and (18, 30) is a direct variation function with a constant of variation of 1.8.

Explanation:

In this case, we have a linear function. We can determine this by checking if the changes between the x-values and the y-values are consistent. For the change in x-values: (14-10 is 4) and (18-14 is also 4), the change is constant. Similarly, check the change in y-values: (24-18 is 6) and (30-24 is also 6), thus the change is constant. Hence, the function is linear.

More so, this function is a direct variation function because it passes through the origin. In direct variation functions, the ratio of y to x remains constant. In this case, the y divided by x at each point [(18/10=1.8), (24/14=1.71), (30/18=1.67)] is approximately 1.8, which is almost constant.

So, the best description of this function is: 'The function is a direct variation function with a constant of variation of 1.8'.

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Answer:

The function is linear but not a direct variation function.

Step-by-step explanation:

Find the volume of a sphere with a radius of 100yd . Express your answer in terms of pi.

Answers

Answer:

4/3*100^3*π

Step-by-step explanation:

V = 4/3*π*r^3

= 4/3*π*100^3

≈ 4.18879*10^6

7 pencils for 16 dollars

Answers

Answer:44 cents

Step-by-step explanation:

7/16 = .4375

Answer:

Step-by-step explanation: To find the unit price you could divide 7 by 16

y is inversely proportional to the square of x.
A table of values for x and y is shown.

a) Express y in terms of x.
b) Work out the positive value of x when y = 25

Answers

Answer:

a) [tex]y=\frac{K}{x^{2} }[/tex]b) [tex]x=\frac{2}{5}[/tex]

Step-by-step explanation:

If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like

[tex]y=\frac{K}{x^{2} }[/tex]

Where [tex]K[/tex] is the constant of propotionality.

Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]

[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]

Replacing this constant, the expression between variables is

[tex]y=\frac{4}{x^{2} }[/tex]

Which is the answer to a).

Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be

[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]

Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]

Final answer:

In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.

Explanation:

In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.

To express y in terms of x, we can rearrange the equation as y = k/(x^2).

To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).

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Find the percentage of vacationers from
question 10 who spent between $1500
and $2000.

Answers

Answer:

The percentage change of vacationers is 33.3 %

Step-by-step explanation:

Given as :

The old value of the vacationers = $ 1500

The new value of the vacationers = $ 2000

Let the percentage variation = x %

Or, x % increase = [tex]\dfrac{\tyextrm new value - \textrm old value}{\textrm old value}[/tex] × 100

Or,  x % increase = [tex]\dfrac{\tyextrm $ 2000 - \textrm $ 1500}{\textrm $ 1500}[/tex] × 100

Or, x % increase = [tex]\frac{500}{1500}[/tex] × 100

Or, x % increase = [tex]\frac{1}{3}[/tex] × 100

Or, x % increase = [tex]\frac{100}{3}[/tex]

∴  x  = 33.3 %

So, The percentage increase change is 33.3 %

Hence The percentage change of vacationers is 33.3 %   Answer

Distribute the expression.

5(2s2−3s+4)

Answers

Answer:

10s^2-15s+20

Step-by-step explanation:

because 5(2s^2)=10s^2, 5(-3s)=-15s, and 5(4)=20

hope it helps:)

Answer:102−15+20

Step-by-step explanation:that’s that answer because I just did the question on imagine math

Which of the following is true of vertex-edge graphs?


(1)They can model real-world problems.
(2)They can all be solved.
(3)Euler paths are the same as Hamilton paths.
(4)All vertices must be used once in Hamilton circuits.

Answers

The answer would be 2 they can all be solved

What is the value of the product (3-2)(3 + 2)?
O 5
O 9+ 41
O 9-4
O 13

Please help

Answers

Answer:

5

Step-by-step explanation:

3 - 2 = 1

3 + 2 =5

5 x 1 =5


1. The enrollment of a school in 2000 was 1200.
Since then, It has increased at a rate of 35
students per year. Write an equation to
represent the enrollment of the school each
year after 2000. Identify your variables. a) What is the rate of change?
b) What is the initial value
c) What is the independent variable?
d) What is the dependent variable

Answers

Answer:

equation: y=35x+1200

a) the rate of change is 35.

b) 1200.

c) The Independent Variable is amount of students per year.

d) The Dependent Variable is the year

I'm not sure about the dependent varaliable, so don't take my word.

a) The rate of change is 35 students per year.

b) The initial value is 1200 students.

c) The independent variable is "x," which represents the number of years since 2000.

d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.

Identifing The Variables.

Set up an equation to represent the enrollment of the school each year after 2000.

We can use the form of a linear equation, where "y" represents the enrollment in a given year (after 2000), and "x" represents the number of years since 2000.

a) Rate of Change (Slope):

The rate of change, which represents how much the enrollment increases each year, is 35 students per year.

b) Initial Value (y-intercept):

In the year 2000, the enrollment was 1200 students.

Therefore, initial value (the value of "y" when "x" is 0) is 1200.

c) Independent Variable: The independent variable, "x," represents the number of years since 2000.

d) Dependent Variable: The dependent variable, "y," represents the enrollment of the school each year after 2000.

We can write the equation:

y = 35x + 1200

a) The rate of change is 35 students per year.

b) The initial value is 1200 students.

c) The independent variable is "x," which represents the number of years since 2000.

d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.

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There are 450 students, 20 teachers and 5 teacher's aides at Canyon Hills Middle School. What is the ratio of students to teachers and their aides?
A
9:2

B
90:1

C
1:18

D
18:1

Answers

Answer:

D. 18 : 1

Step-by-step explanation:

Students : teachers and aides

450 : 25

Treat it like a fraction. 450 over 25 simplifies to 18 over 1 because 450/25=18 and 25/25=1.

Therefore, the ratio is 18 : 1

Answer: 18:1

Step-by-step explanation:

450 students : 25 teachers

18 students : 1 teachers

450/25= 18

Jimmy measured four pieces of wood. their measures are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft. what's the length of the shortest piece​

Answers

9/2= 4.5 ft
4 2/9= 4.22
4.02, 4.2, 4.22, 4.5
4.02 feet is the shortest length of wood out of throws four pieces

After converting all measurements to the same format (decimals), we can see that the shortest piece of wood Jimmy measured is 4.02 ft.

To find the shortest piece of wood, we first need to convert all the lengths to the same format, preferably in decimals for easier comparison. The lengths of the wood pieces given are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft.

Let's break it down:

4.2ft remains as it is. 9/2ft equals 4.5ft when converted to a decimal. 4.02ft remains as it is. 4 2/9ft equals approximately 4.22ft when the fraction is converted to a decimal.

So, we have pieces of wood that are 4.2 ft, 4.5 ft, 4.02 ft, and 4.22ft. Looking at these numbers, it is clear that the piece of wood that measures 4.02 ft is the shortest.

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Which is an example of the relationship between the arts andsocial change during the 1920s?answer is c the Great Migration lefted the south with a severe lack of the low wage workers and many companies went out of business as a result Demand for a certain product is forecast to be 800 units per month, averaged over all 12 months of the year. The product follows a seasonal pattern, for which the January monthly index is 0.8. What is the seasonally-adjusted sales forecast for January? please solve much appreciated A 16 year old highschool student presents in the ER with a fever, stiff neck, headache and nausea. You order a spinal tap to be performed. Gram staining of the CSF reveals Gram (-) rods under the microscope. Which orgainism do you suspect is the likely causative agent? Which triangle congruence postulate proves these two triangle are congruent?A. AASB. HL C. SAS D. ASAPlease answer this During the Second Punic War, the Carthaginian general Hannibal: a. brought his entire army, including elephants, over the Alps. b. was defeated by Roman armies at the battle of Tours in France. c. became the last foreign invader to fight on Romes home territories. d. defeated the Roman general Maxentius at the battle of the Milvian Bridge in Rome. A specific territory or zone that has laws and regulations different from the rest of the country is called a(n) What mass of FeSO4^2- x 6H20 (Molar Mass=260g/mol) is required to produce 500 mL of a .10M iron (II) sulfate solution. A.) 9g B.) 13g C.) 36g D.) 72g Mia ordered five DVDs, all at the same price, from an online retailer. There was a shipping charge of $14.50 for the complete order but no sales tax. If Mias total charge for her order was $79.45, what was the price of each DVD? Kian has been asked to create a company logo to be put on all company merchandise. The logo needs to be contained within a rectangular space that is 2 inches wide and 3 inches long. How much space does Kian have to work with:5 units5 inches6 square inches6 cubic inches Explain the properties of water and why it is important to life. Include the following: specific heat, density, polarity, Universal solvent y-2=-(x+7) rewrite in standard form Jenna was raised by loving, devoted parents who always encouraged her to do her best and who appreciated her efforts. As a result, Jenna has high self-esteem. When she begins her first year of college, she is MOST likely to ________. Mr. Hector Joules presents to the office today for swelling in his right testicle. The swelling has been present for the past month. He reports orchialgia, described as a dull ache in the testicle. He also has had a feeling of heaviness in his abdomen. He hasnt had any recent injury to the area. He denies risky sexual behavior, urethrorrhea, dysuria, nocturia, polyuria.Which symptom is exhibited by Mr. Joules? Which word equation summarizes the hydrolysis of a carbohydrate please explain, but not to wordy Find the absolute extrema of f(x) = e^{x^2+2x}f ( x ) = e x 2 + 2 x on the interval [-2,2][ 2 , 2 ] first and then use the comparison property to find the lower and upper bounds for I = \displaystyle \int_{-2}^{2} f(x) \, dxI = 2 2 f ( x ) d x. It takes 12 hours for 7 men to paint a room.How many men would be needed to paint the room in 3 hours? PLEASE HELP Answer all three of the questions below.1. Write an equivalent expression to 2 + 3 + 5 + 6 by combining like terms.2. Find the sum of (8a 2b - 4) and (3b 5).3.Write the expression in standard form: 4(2a) + 7(4b) + (3 c 5). Write the quadratic equation whose roots are -2 and 1, and whose leading coefficient is 4 .