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

HELP WITH MY MATH EXAM i don't know what to do and my head hurts a lot

Answers

Answer:

x = 154/13

Step-by-step explanation:

You are given the measures of all three angles in a triangle

so according to the Triangle Sum Theorem:

∠MNO + ∠OMN + ∠NOP = 180

1. Substitute the measures of the angles into the equation:

(3x + 11) + (2x + 20) + (8x - 5) = 180

2. Combine like terms:

(3x + 2x + 8x) + (11 + 20 -5) = 180

13x + 26 = 180

3. Isolate x by subtratcing 26 from both sides

13x + 26 -26 = 180 -26

13x  = 154

4. Solve for x by dividing both sides by 13

13x/13 = 154/13

x = 154/13

Which graph matches the following inequality: y<-2/5x+1?

Answers

Answer: B is the answer

Step-by-step explanation:

Mike completed an online course that contained 20 core topics in a total of
40 learning hours. How many topics did he complete in 12 hours time?

Answers

Answer:

6 hours

Step-by-step explanation:

What you have to do is find the unit rate, which would be 20/40 which is .5 ( half an hour, 30 mins ) . Then you would do 30 x 12 = 360 ( 6 hours ).

Find f(-5) if f(x) = |x + 1|.
A)6
B)5
C)4

Answers

The answer would be C)5

Your bank account has a balance of $25. You withdraw $46. You then deposit $50. What is your new balance?

Answers

Answer:29

Step-by-step explanation:$25-$46=-21

-21+50=29

$29

25-46=-21
-21+50=29

Which statement about residual plots is not true?


A. if the residuals are randomly distributed, the model is probably reasonable


B. The sum of the residuals is 0


C. The vertical axis shows residuals


D. The horizontal axis shows the predicted y-values

Answers

Answer:

The horizontal axis shows the predicted y-values.

Step-by-step explanation:

The person above me is dumb, he's cancelled.

Answer:

D

Step-by-step explanation:

y^2+3y^2-6y+y^{3-8y}

Answers

Answer:
Wdym? BENCNDNF

Can somebody help me plz with this math problem!!

Answers

Answer:

Step-by-step explanation:

.

Answer:

thxxxxxxxxxx for the points

Step-by-step explanation:

Evaluate each of the following expressions for
a = -2 and b = -10
1. ab


Answers

answer: 20
Explanation: it’s 20 because when 2 variables are together it automatically multiples and when you have 2 negatives they become positives

Write 3.19×10−2 in standard form.

Answers

Answer:

It is already in standard form

What is the temperature displayed on the thermometer?

Answers

Your Answer :

98.6°F (37°C).

Step - By - Step Explanation :

Your normal body temperature should be around 98.6°F (37°C). If you have a temperature that is over than 100.4°F (37.2°C), then you should see your doctor preferably soon.

Note :

I am sorry if this is the wrong answer to your question. Your query did not have an image to display the temperature on the thermometer nor did your query have any further context for us to examine.

Good luck on your homework and have a great day.

Feel free to comment on my answer if you have any further questions.

Answer:

25

Step-by-step explanation:

It's Correct On Edge As Well :P

carlos read 40 pages of a book in 50 minutes. how many pages should he be able to read in 80 minutes​

Answers

Answer:

70

Step-by-step explanation

what is 3600x0+1=2?
thanks i appreciate it

Answers

Answer:

actually it = 1 but there's your answrr

Step-by-step explanation:

3600x0 = 0

0+1=1

Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 13, adjacent B C is 5, opposite A C is 12.
For the triangle above, find sin B.
a.
25°
c.
0.923
b.
0.385
d.
18°

Answers

Answer:

sin = opp/hyp

sin B = 12/13

sin B = 0.923

C

W=ab/a+b ; solve for a

Answers

I could solve for a and it said this:

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

All real numbers

Interval Notation:

(−∞,∞)

But I can solve for W and B

W  =  2b

b = W/2

a = I could solve for a and they put the answer to this (−∞,∞)

The princiole labeled some of the marks on the four thermometers with dollar amounts. Decide what labels belong on the remaining marks​

Answers

Answer:

hmm lets see

Step-by-step explanation:

у = 2х - 5
Х
у

0
1
2
3
4

Answers

Answer:2x-5= -10

If that was what you mean.

Step-by-step explanation:

Answer:

y = -5

y = -3

y = -1

y = 1

y = 3

Step-by-step explanation:

What is the additive Inverse (zero pair) of 3k

Answers

Answer:

-3000

Step-by-step explanation:

an additive inverse of a number is a number, when added to, makes zero. So if its 3000 than the inverse would be -3000 since it equal 0

Ayuda por favor es para una tarea!!

Answers

Answer:

m<PAT = 41°

m<TAY = 41°

ASAP 50 POINTS Which expression is a sum of cubes? -64x6y12+125x16y3 -32x6y12+125x16y3 32x6y12+125x9y3 64x6y12+125x9y3

Answers

Answer:

64x6y12+125x9y3 I think. Hope this helps

Answer:

The answer is D

64x6y12+125x9y3

Step-by-step explanation:

Youre welcome

What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec2(θ) = 1 + tan2(θ).)

Answers

9514 1404 393

Answer:

  43.303°

Step-by-step explanation:

Problem geometry varies. For this question, we will assume ...

The ball is launched at a 53° angle, 24 m from a buildingThe ball takes 2.20 seconds to reach the buildingThe railing is 6.4 m high

The equation of motion in this case is ...

  h(x, α) = x(tan(α) -4.9x/(v·cos(α))²)

where h(x) = height at distance x, α is the launch angle, vₓ is the horizontal speed of the ball.

__

The ball was launched at an angle of 53° in part (a) at a speed that gives it a horizontal speed of (24 m)/(2.2 s). That is, the speed in the direction of launch is ...

  (24 m)/(2.2 s)/cos(53°) ≈ 18.126983 m/s . . . . speed in part (a)

__

For the question at hand, we need to find α such that ...

  h(24) = 6.4

Substituting into the above equation gives ...

  6.4 = 24(tan(α) -24(4.9/18.126983^2·sec(α)^2)

  6.4 = 24(tan(α) -0.35789551(tan(α)^2 +1)) . . . . replacing sec(α) using hint

If we let z represent tan(α), this can be written in standard form as ...

  8.5894922·z^2 -24z +14.989492 = 0

Then the minimum solution (by the quadratic formula) is ...

  z = (24 -√(24^2 -4(8.5894922)(14.989492)))/(2·8.5894922)

  z = 0.94244774

And the angle is ...

  α = arctan(z) = arctan(0.94244774) ≈ 43.303°

The teacher must launch the ball at an angle of at least 43.3° to clear the railing.

Which of the following fraction pairs are equivalent fractions? *
a. 1⁄4 and 1⁄2
b. 1⁄4 and 3⁄4
c. 1⁄4 and 4⁄12
d. 1⁄4 and 8⁄32

Answers

Answer:

D. 1/4 and 8/32

Step-by-step explanation:

its d because if you simplify 8/32 you get 1/4

Horizontal lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase left angle is 75 degrees. At the intersection of lines b and e, the uppercase right angle is 115 degrees. At the intersection of lines a and f, the bottom right angle is 75 degrees.

Which lines are parallel? Justify your answer.


Lines a and b are parallel because their alternate exterior angles are congruent.

Lines a and b are parallel because their same side exterior angles are supplementary.

Lines e and f are parallel because their alternate exterior angles are congruent.

Lines e and f are parallel because their same side exterior angles are congruent.

Answers

Lines e and f are parallel because their alternate exterior angle is congruent. Option C is correct.

Find the diagram attached;

The point where two lines meet is known as an angle.

From the given diagram, we can see that the angle of 75 degrees is at the top left corner is similar to the 75 degrees down right.

Hence we can conclude that lines e and f are parallel because their alternate exterior angle is congruent.

Learn more here: https://brainly.com/question/11397920

Answer: Option 3 or C. Lines e and f are parallel because their alternate exterior angles are congruent.

Step-by-step explanation: The correct answer is C.  

I got it right on the Edge 2022 quiz. Trust me the proof is shown below.

5. Ameris rolls a standard number cube with the numbers 1-6. What is the probability of
rolling a 6 or a 2?
a. 16
b. 13
C.
d. 5%

Answers

Answer: its 2/6 is the answer the choices don't make cense

Step-by-step explanation:

Vincent counts 30 dimes and 87 pennies in a bowl. How many more pennies
than dimes are in the bowl?

Answers

Answer:

57

Step-by-step explanation:

87-30=57. That means that there are 57 more pennies than dimes in the bowl.

Answer:

subtract 30 from 87

Step-by-step explanation:

87-30

Angle ABD is 90 what is the measure of ABC

Answers

Answer:

90 I am guessing. if it's like a square or rectangle

Write the equation of the parabola in vertex form.
vertex (4.1), point (3,-4)

Answers

Answer:

              [tex]\boxed{\bold{y=-5(x-4)^2+1}}[/tex]

Step-by-step explanation:

[tex]y=a(x-h)^2+k[/tex]    - vertex form of equation of a parabola where vertex is (h,k)

[tex]y=a(x-4)^2+1[/tex]  - vertex form of equation of a parabola where vertex is (4,1)

The parabola goes through point (3, -4) so if x=3 then y=-4

[tex]-4=a(3-4)^2+1\\\\-4-1=a(-1)^2+1-1\\\\-5=a\cdot1\\\\{}\ \ a=-5[/tex]

Therefore the equation of the parabola in vertex form with vertex (4,1), going through point (3,-4):

[tex]y=-5(x-4)^2+1[/tex]

What is equivalent to

Answers

The answer is 3 with a little 7. Alternatively 2187

Helen borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000 and an interest of $1,200. What was the annual interest rate?

Answers

Answer:

3%

Step-by-step explanation:

No explanation

HELP! DUE TONIGHT!! Also, I need an explanation (if you can its alright if not) so I can also understand it for the test too.

What is the value of x?

Answers

Answer:

The value of x in the problem is 1.

Other Questions
5. Which of the following can be used to create emphasis in a composition? A. Color B. Shape C. Orientation D. All of the above 50 BRAINLY POINTS PLS HELP A Paco no le gustan estas pinturas porque l no ___________ el arte de los siglos pasados.A. comprendesB. comprendeC. comprendoD. comprenden FAST PLS I HAVE TO PRESENT AND I WANNA KNOW IF THIS IS CORRECT ILL GIVE BRAIN THING TO 1ST PERSON(in german)"Majka doesn't like to ski"-Majka spielt nicht gern skipls tell me if its right lol Explain: How is presidential and parliamentary both forms of democracy?Your answerHelp !!!! A car with a mass of 800 kg is accelerated with a force of 6000 N. If resisting forces are ignored, what is the acceleration of the car? yen Value of a mixed stream Harte Systems, Inc., a maker of electronic survillance equipment, is considering selling the rights to market its home security system to a well-known hardware chain. The proposed deal calls for the hardware chain to pay Harte $28 comma 000 and $23 comma 000 at the end of years 1 and 2 and to make annual year-end payments of $18 comma 000 in years 3 through 9. A final payment to Harte of $30 comma 000 would be due at the end of year 10. a. Select the time line that represents the cash flows involved in the offer. Maya tells Starr the real reason Hailey quit following her on Tumblr. What was Plzzzzzzzz heeeelllppp Determine whether the following symbols are universal or contextual. In "The Nightingale and the Rose," Oscar Wilde uses a red rose as a symbol for love. In To Kill a Mockingbird, Harper Lee uses a mockingbird as a symbol for innocence. In A Little Princess, Frances Hodgson Burnett uses hot buns as a symbol for the connection between the main character and a poor street child. In "The Water of Life," the Brothers Grimm use water as a symbol for life. How do ballot amendments influence our political system? Select ALL of the events that were important to Jamestown and to the future of British America in 1619.[] Destruction of the Powhatan Indians[] Conflict with France[] First Africans arrived in the colony[] First elected lawmakers[] First labor strike for rights[] English settlers can own land after 7 years of labor[] Large numbers of women arrive in the colony[] Many settlers left the New World to return to England Of the 52 cards in the deck, four are aces and others (kings, queens, jacks, and tens) are worth 10 points each. The dealer has a blackjack if one card is an ace and the other is worth 10 points; it doesn't matter which card is face up and which card is face down. How many different blackjack hands are there? Help plz I need it ASAP give poinys Determine if the sequence 2, 8, 17, 29, ... is arithmetic. If it is, determine the first term a and the common difference d.Is the sequence 2, 8, 17, 29, ... arithmetic? 26 - x = 17 What does x equal? How do you know family membersare more comfortable in the housenow?D. They are sitting at the kitchen table,They hear a loud creak.Dad has pounded in his last nail.O Blake says she is used to the place. 1. The amount of area covered by blackberry bushes in a park has beengrowing by 12% each year. It is estimated that the area covered in 2009was 4,500 square feet. Estimate the area that will be covered in 2020. Alma was given some money as a gift and deposited it into a savings account. She makes a withdrawal of the same amount at the end of each month. At the end of the 5th month, her balance was $442. At the end of the 13th month, her balance was $226. a. What is the major evolutionary advantage to producing an amnion? b. What does that mean for embryonic development for the animal phylum as compared to the animal phyla?