A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet away from the player. The height $y$y​ (in feet) of a second hockey puck is modeled by $y=x\left(0.15-0.001x\right)$y=x(0.15−0.001x)​ , where x$x$x​ is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.

Answers

Answer 1

Answer:

The maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels further  

Also the distance of the maximum height of first pluck from the player is less than the distance of the second pluck from the player hence the second pluck travels further

Step-by-step explanation:

From the question we are told that

  The maximum height of the first pluck is  [tex]h_1 = 3 \ ft[/tex]

   The height of the second height is mathematically represented as

              [tex]$y=x\left(0.15-0.001x\right)[/tex]

=>           [tex]y=0.15x -0.001x^2[/tex]

Generally at maximum height  [tex]y' = 0[/tex]

So

      [tex]y'=0.15 -0.002 x = 0[/tex]

=>    [tex]x =  75 \  ft [/tex]

Here 75 ft is the horizontal distance the second pluck traveled at maximum height

   So the maximum height of the second pluck is mathematically represented as

       [tex]y=0.15(75) -0.001(75)^2[/tex]

=>     [tex]y=  5.625 \  ft [/tex]  

So comparing the maximum height  of the first and the second pluck we see that the maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels father


Related Questions

3(2x+4)=-18
What is x and how do you solve

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Answer:

x=1

Step-by-step explanation:

divide by 3 and then -4 and then divide by 2

A savings account balance can be modeled by the graph of the linear function shown on the grid.

What is the rate of change with respect to the number of deposits?
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2) 100 per deposit
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Answer:

5:15 is the ratio for the amount of circles to total shapes.

Step-by-step explanation:

There are 5 circles and 15 shapes total.

So the ratio of circle to the total amount of shapes is 5:15

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Answer:

its C :)

Step-by-step explanation:

What is the value of x?
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12x + 14

Answers

Answer:

[tex] \frac{14 }{3} [/tex]

Step-by-step explanation:

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x=

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M= 1/2
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M= -1/2
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Answers

Answer:

It should be 1/2

Step-by-step explanation:

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PLEASE HELP A GIRL OUT !!!!!!! UwU
Explain how to write a linear equation from a word problem in the slope-intercept form. Explain in detail what words you are looking for in the problem. Use complete sentences. Must inlclude capital letters and punctuation where needed.

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It depends on the problem, but here's an example.

Let's say you earn $20 an hour and you already have $100 in the bank. If you work x hours, then you'll have 20x additional dollars on top of the $100 you already have. So in total you have y = 20x+100 dollars

x = number of hours worked

y = total amount of money

This does not take into account taxes or other kinds of fees/deductions from your paycheck.

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The slope tells us how fast the money increases (since it's the rate of change). In this case, slope = rise/run = 20/1 meaning that for each hour, the money goes up by $20.

The y intercept is the starting value which in this case is $100. If you worked x = 0 hours, then you'll still have that $100.

Edwin and Anthony are building a rectangular deck in their backyard.The Longer side is 2 more than 1/3 the perimeter. The shorter side is 1/10 of the perimeter. Know that the longer side is 9 ft longer than the shorter side. What is the Perimeter of the deck?

Answers

Answer: The perimeter is 30ft.

Step-by-step explanation:

Let's define:

L = length of the longer side.

S = length of the shorter side.

P = perimeter

we know that for a common rectangle:

P = 2*S + 2*L

We aso know that:

L = 2ft + (1/3)*P

S = (1/10)*P

L = S + 9ft.

So we have a system, let's find the perimeter only using this system (So i will ignore the equation for the perimeter of a rectangle)

First, we can replace the third equation in the first equation, now we have a system with only two equations:

S + 9ft = 2ft + (1/3)*P

S = P/10

Now we can replace the second equation in the first equation, and get:

P/10 + 9ft = 2ft + P/3

Now let's solve this for P.

9ft - 2 ft = P/3 - P/10

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(30/7)*7ft = P = 30ft.

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Unit Imaginary Number

The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.

Write the number in scientific notation: 0.00000199?

Answers

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

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×

10

6

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Trace is at school and wants to send his homing piaeon home for his forgotten Geometry homework. If the coordinates for his home are (-5,5) and his school is at (-1,2), what is the length of his pigeon's flight directly to the house?
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Answers

Answer:

5 units

Step-by-step explanation:

From the coordinates, we have;

x1 = -5

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Plugging in the relevant values, we have;

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d = √(16 + 9)

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Answer:

1. Two angles are called complementary when their measures add to 90 degrees.

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Step-by-step explanation:

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Answers

Answer:

1.98 x 10³  

Step-by-step explanation:

1980  

= 1.98 x 1000   (note 1000 can be written as 10³)

= 1.98 x 10³   (answer)

What is the answer to 3n/7 = 33/70

Answers

Answer: [tex]n=\frac{11}{10}[/tex]



Step-by-step explanation:

[tex]\frac{3n}{7}=\frac{33}{70}[/tex]

[tex]\frac{210n}{210}=\frac{231}{210}[/tex]

[tex]n=\frac{11}{10}[/tex]

Lol this question seems simple for a person coming from Calculus only to increase my confidence ; )

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n = 11/10

Which of the statements is also true in Spherical geometry?

Answers

I think all of them are true

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Write an addition problem to represent the changing amounts of money Dalaya has.
Find the amount of money Dalaya has by the end of Friday. Show your work to justify your answer.

Answers

Answer:

15-12+5.5+3-8

 

Step-by-step explanation:

15-12=3

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Answer:

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Step-by-step explanation:

You write the equation first and then find the answer.

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Answers

Answer:

It is rational because the answer is -3

Step-by-step explanation:

-3 can be writen as a fraction so it is a rational number.

Answer:

That is a rational number

Step-by-step explanation:

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Answers

m = -9/8 (slope)

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_________________________

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Answers

No correlation towards each other

pic below................................
answer ASAP

Answers

Answer:

The answer is C.-216

Step-by-step explanation:

Answer:

C.)-216

Step-by-step explanation:

Since -6 is negative, it makes it become a positive when multiplyed, and then back to a negative when multiplyed again.

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1. $45

2. $18

3. $50

4. $200

Answers

Answer:

50$

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show your work

7(x-8)=2x-31

Answers

Answer:

x=5

Step-by-step explanation:

7 (x-8)=2x-31

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7x-56=2x -31

Drag the 2x over to the other subtracting it from 7x.

7x-2x-56=-31

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Drag the 56 to the other side and add it to -31

5x= -31+56 (or 56-31)

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Hope this helps!!

what is the answer to f(-5)=x^2-5

Answers

Answer:

32

Step-by-step explanation:

Write an equivalent expression to the following: 1/2 (-6x + 8) – 7

Answers

Answer:

-3x -3

If this is not the answer you are looking for plz let me know!!!

Answer:

-6x+8=14

Step-by-step explanation:

1/2*(-6x+8)-7 |+7

1/2*(-6x+8)=7 | ÷1/2

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You mean sth like this?

if y=40 when x=16, find y when x=10.

Answers

Answer:

25

Step-by-step explanation:

Y/10 = 40/16

Y=25

(11x - 1)
(20x – 3)
151°

Answers

Answer:

x= 1.6 degrees

Step-by-step explanation:

to find the missing angle 180 degrees - 151 degrees

29° is the missing angle at the bottom ryt of the triangle.

all angles in triangle add upto 180°

so, 20x-3°+11x-1°+29°= 180°

31x=180°-25°

x= 1.6°

A polygon with three edges and three vertices is called a triangle.

x=1.6° is its value.

Explain about the triangle?

Based on the lengths of its sides, triangles can be categorized into one of three groups: Scalene. Isosceles. Equilateral.

The trigon, a 3-sided polygon, is sometimes (though not often) referred to as a triangle. Every triangle has three sides and three angles, some of which might be the same.

The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180degrees.

To identify the omitted angle between 180 and 151 degrees

The triangle's bottom right corner lacks a 29° angle.

triangle's angles sum up to 180°

so, 20x-3°+11x-1°+29°= 180°

31x=180°-25°

x =1.6 degree

To learn more about triangle refer to:

https://brainly.com/question/17335144

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find the DIFFERENCE between 901.28 and 375.54

Answers

Answer:

Pretty sure its 525.74

At the beginning of the year, John had $40 in savings and saved an additional $13 each week thereafter. Isaac started the year with $80 and saved $9 every week. Let J represent the amount of money John has saved tt weeks after the beginning of the year and let I represent the amount of money Isaac has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until John and Isaac have the same amount of money saved.

Answers

john- 40+t13= j
isaac- 80+t9=i
They would have the same amount of money after 10 weeks
john- 40+(10•13)= 170
isaac- 80+(10•9)= 170
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