A model rocket is launched from the roof of a building. Its flight path is modeled
by h = -5t^2 +30t +10 where h is the height of the rocket above the ground in
metres and r is the time after the launch in seconds.
What is the rocket's maximum height?

Answers

Answer 1

Answer:

55

Step-by-step explanation:

This is the equation of a parabola. To make things simpler, we can replace [tex]h[/tex] with [tex]y[/tex] and [tex]t[/tex] with [tex]x[/tex]. Therefore, [tex]y=-5x^2+30x+10[/tex]. Because the coefficient of the [tex]x^2[/tex] term is negative, we know the parabola points down, and the maximum height is the vertex. The x coordinate of the vertex of a parabola can be found with the equation [tex]-\frac{b}{2a}[/tex], or [tex]-\frac{30}{-10} = 3[/tex]. Plugging in [tex]3[/tex] into the equation gives us [tex]y = -5(3)^2+30(3)+10 = \boxed{55}[/tex]


Related Questions

On Friday, the temperature changes -30 each hour. If the temperature changed for 7 hours, what is the total temperature change?
Please hurry and answer!

Answers

A -120 difference will be seen in the temperature within a 7 hour period

Equation

-30 x 7

Multiplying two of different signs ( - + ,  + - ) will always be negative.

Multiplying two of the same sign ( - - , + + ) will always be positive.

Simplify.

2 ( to the power of 3)+4⋅8




40

80

96

160

Answers

Answer:

2 to the power of 3 is 8 so

8 + 4.8 = 12.8

Step-by-step explanation:

Answer: A, 40

1) simplify 2^3 to 8

8+4•8

2) simplify 4•8 to 32

8+32

3) simplify

40

HELP ASAP. ALGEBRA 1 , ITS EASY. PLEASE HHHHEEEEEEELLLLLPPPPPPPPPP.
Question 1:

9|x/4| -10=8

Question 2:

4+|3x+3|=28

Question 3:

4|x-9|+7=67

Answers

Answer:

Question 1

9|x/4| -10=8 Answer- x= (8,-8)

Question 2

4+|3x+3|=28  Answer- x=(7,-9)

Question 3

4|x-9|+7=67  Answer- x=(24,-6)

Step-by-step explanation:

help me please i need help

Answers

Answer:

I have NO IDEA

Step-by-step explanation:

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1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match. (a) How many schedules are there?

Answers

Complete Question

1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match.

(a) How many schedules are there?

(b) How many schedules include neither sister?

Answer:

a

   [tex]N  =  1,411,200[/tex]

b

  [tex]M  =  302, 400[/tex]

Step-by-step explanation:

From the question we are told that

   The  number of players in Taft High School is t =  8

    The  number of players in McKinley High School  is k = 7

   The number of rounds is  n  =  4

   The highest number of match each player can play is  w =  1

   

Generally the total number of schedules is  

      [tex]N  = ^tP_4 * ^k P_4[/tex]

      [tex]N  = ^8P_4 * ^7 P_4[/tex]

=>   [tex]N  =  \frac{8!}{(8-4)!} * \frac{7!}{(7-4)!}[/tex]

=>   [tex]N  =  \frac{8!}{4!} * \frac{7!}{3!}[/tex]

=>  [tex]N  =  \frac{8*7 *6*5*4*3*2*1}{4*3*2*1} * \frac{7*6*5*4*3*2*1}{3*2*1}[/tex]

=>  [tex]N  =  1,411,200[/tex]

Generally the  number of schedules that include neither of the sisters is  mathematically represented as

        [tex]M= \ ^{t-1}P_4 *\ ^ {k-1} P_4[/tex]

        [tex]M= \ ^{8-1}P_4 *\ ^ {7-1} P_4[/tex]

=>    [tex]M= \ ^{7}P_4 *\ ^ {6} P_4[/tex]

=>     [tex]M  =  \frac{7!}{(7-4)!} * \frac{6!}{(6-4)!}[/tex]

=>     [tex]M  =  \frac{7!}{3!} * \frac{6!}{2!}[/tex]

=>     [tex]M  =  \frac{7 *6*5*4*3*2*1}{3*2*1} * \frac{6*5*4*3*2*1}{2*1}[/tex]

=>      [tex]M  =  302, 400[/tex]

Bernard a part of a small pizza he started with 11/12 of a pizza but only ate 2/3 of it which is the best estimate of the amount Bernard ate?

Answers

Answer:

Bernard ate a little less than Two-thirds of the pizza.

Step-by-step explanation:

i took the test

Answer:

c 2/3

Step-by-step explanation:Bernard ate part of a small pizza. He started with StartFraction 11 Over 12 EndFraction of a pizza but only ate Two-thirds of it. Which is the best estimate of the amount Bernard ate?as u can see it said HOW many did he eat he ate 2/3 of it your welcome friend!

Pls help me 8th grade math pls solve all the problems correctly

Answers

Answer:

A.$12

B.$4.5

C.4.5$ per game + 12$

Step-by-step explanation:

It shows the first payment being 12$ so A is 12$

then it goes up to 16.5$ so

16.5-12= 4.5$

So 4.5$ per game.

C. 4.5$ per game + 12$

A. 12$
B. 4.5$ per game
C. c = 4.5g + 12

What is 9/7 times -9/5?

Answers

Answer:

- 2 11/35

Step-by-step explanation:

Step 1:

9/7 × - 9/5     Equation

Step 2:

- 81/35      Multiply

Answer:

- 2 11/35       Convert

Hope This Helps :)

Answer:

Step-by-step explanation:

nevermind sry

I need help with this can anyone give me the answer

Answers

Translation (-1, -3), option B

Please help me i will give all of my points 14
Please help i need this right now

Answers

Answer:

3 7/12

Step-by-step explanation:

What is 7/9 x 21/10=

Answers

Answer:

1 19/30

Step-by-step explanation:

Just multiply and cross simplify

7/9 x 21/10

9 and 21 can be simplified to 3/7

7/3 x 7/10

Multiply from left to right

49/30

1 19/30

Answer: 1.63333333333

7/9 = 0.77777777777

(7/9) * 21 = 16.3333333333

((7/9) * 21)/10 = 1.63333333333

You have 8 quarts of brown stock.
You need 3 cups to make one serving of braised short ribs.
How many servings can you make?
(don't include partial portions)​

Answers

Answer:

you can make 10 servings

Step-by-step explanation:

Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes. That is to say, if one line has slopem1and the other has slopem2thenm1 · m2 = −1.Please note that a horizontal line is perpendicular to a vertical line and vice versa, so we assumem1 ≠ 0andm2 ≠ 0.Below, you are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point.

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is [tex]y = -4 x[/tex]

Step-by-step explanation:

From the question we are told that

The line is [tex]y = \frac{1}{4} x + 8[/tex]

The point is P(0,0 )

Generally the equation for a line is [tex]yn = mx + c[/tex]

Now comparing this with the given equation we see that

[tex]m =\frac{1}{4} = slope[/tex]

[tex]C =8 = intercept [/tex]

Generally the slope of the perpendicular to the given line is mathematically evaluated as

[tex]m_1 = - \frac{1}{m}[/tex]

=> [tex]m_1 = - \frac{1}{ \frac{1}{4}}[/tex]

=> [tex]m_1 = -4 [/tex]

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and [tex]m_1 = -4[/tex] is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

[tex]y = -4 x[/tex]

If y= 44 when x=240, what is the value of y when x=84?

Answers

y = 15.4

i just found the scale factor between the two (5.4545) and divided 84 by that
15.4 , I think that would be the answer for ur question

15.03 cm, 14.92 cm, and 15.30 cm. The actual length is 15cm. Which of the following would be most accurate?
FIRST TO ANSWER GETS BRAINLIEST!!!

Answers

Answer:

14.92 ^-^

Step-by-step explanation:

What must be true of the boundary lines in a system of two linear inequalities if there is no solution of the system? Explain.

Answers

Answer:

have you check google or try mathaway or slander

Toby plans to enroll for 2 semesters per year of college. How can he calculate the extra mo ey he needs for each semester? What is the amount that he needs per semester?

Answers

Hey there!

Sorry if I answered your question too late, but here is the answer!

Step-by-step explanation:

Toby will require $2,000 for expenses for one year of college. He plans to enroll for 2 semesters per year, so Toby has to divide $2,000 by 2 to find the expenses for each semester. He can set up the division as $2,000 ÷ 2 or 2 ⟌2,000.

Answer: He will need $1,000 for each semester.

You are free to use the Step-by-step explanation to show your work. Have a great day! :))

Solve x^2 – 7x = -13.

Answers

Answer:

No solutions I think

Step-by-step explanation:

Negative seven is less than negative six.
True or False

Answers

Answer:

true

Step-by-step explanation:

negatives keep getting smaller and smaller

Answer:

false

Step-by-step explanation:

negative 6 is bigger because its closer to a whole number (integer which is bigger) so it has more value

What is the perimeter of a hexagon with a side length of 31cm?

Answers

Answer:

186cm im pretty sure

Step-by-step explanation:

Answer:

The perimeter is 186 centimeters.

Step-by-step explanation:

The perimeter is the combination of all the side lengths of a figure. So, to figure this one out, it would be:

31 + 31 + 31 + 31 + 31 + 31

Or in simpler terms:

31 times 6.

All you need to do is multiply, and the answer comes out to 186cm

The total dinner bill for 5 people was 55.30. How much will each person pay if they share the cost equally

Answers

Answer:

11.06

Step-by-step explanation:

55.30/5 Separate the decimals and whole numbers and divide both by 5

55/5=11 and 0.30/5=0.06

11+0.06=11.06

Answer:

11.06

Step-by-step explanation:

Question
The force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot-
long board. How many pounds of pressure is needed to break a 5-foot-long board?
Provide your answer below:

Answers

Answer:

9.6

Step-by-step explanation:

60 pounds of pressure is needed to break a 5-foot-long board,

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Richard uses 24 pounds of pressure to break a 2-foot-long board.

How many pounds of pressure is needed to break a 5-foot-long board,

we have to find.

i.e. 24/2 * 5

   =12*5

  =60

hence, 60 pounds of pressure is needed to break a 5-foot-long board,

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ2

What values make d^2=36 a true number sentence

Answers

Answer:

6

Step-by-step explanation:

becuase 6^2 equals 36

Answer:

d=6

Step-by-step explanation:

Use the inverse operation of square roots

find the value of x. The answer is 53, but I need to show my work.

THANK YOU!!!

Answers

Answer:

53

Step-by-step explanation:

so first sutract the large angle from 360:

360 - 213 = 147

then subtract the other large known angle:

147 - 107 = 40

now we know the x - 13 = 40 so to find x we just have to add 13:

40 + 13 = 53

The answer to the question is 53.

what is the value of n n+11=13​

Answers

Answer:

n = 2

Step-by-step explanation:

[tex]n + 11 = 13[/tex]

Subtract 11 from both sides to isolate n.

[tex]n + 11 - 11 = 13 - 11[/tex]

[tex]n = 2[/tex]

HURRY HELP ME select ALL the correct answers
A sailboat travels a distance of 2 1/2 miles in 1/6 of an hour. which complex fraction represents the unit rate in miles per hour?

Answers

It’s the 2nd one :)















a turtle is moving along a straight line a constant rate it moves 2/7 of a mile 3/5 of an hour

Answers

Answer:

0.2miles at 12minutes

Brad had 72 bargain baseballs. What is the total price for the bargain baseballs if each ball is $9

Answers

Answer:

648

Step-by-step explanation:

9 times 27

Answer:

$8.

Step-by-step explanation:

72 divided by 9

hope this helped </3

Round 733,712 to the nearest thousand
733,712 ~

Answers

Answer:

734,000

Step-by-step explanation:

The thousands digit is the fourth digit from the right (1000) so we start by underlining that digit.

733,712

Look at the digit to the right of the underlined digit. If the number is 5 or more, add one to the underlined digit. Since 7 is 5 or more, we add one to the underlined digit.

All of the digits behind the underlined digits turn to zeros to hold the place values.

734,000

What is the domain of H

Answers

Answer:

X ∈ {-2, -1 ,1 ,5 ,6}

Step-by-step explanation:

Answer:

Step-by-step explanation:

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