1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stella [2.4K]
3 years ago
10

A rocket is fired with an initial vertical velocity of 40 m/s from a launch pad 45 m high, and its height is given by the formul

a -5t^2+40t+45 where h is in meters and t is in seconds. How high does the rocket go? How much time is the rocket in flight?
Mathematics
1 answer:
N76 [4]3 years ago
6 0

Answer:

1) 125 meters

2) For 9 seconds.

Step-by-step explanation:

The rocket's height is given by the formula -5t^2+40t+45.

Notice that this is a quadratic.

Part 1)

Since this is a quadratic, the highest height the rocket goes will be the vertex of our quadratic. Remember that the vertex of a quadratic in standard form is:

(-\frac{b}{2a}, f(-\frac{b}{2a}))

So, let's identify our coefficients. The standard quadratic form is:

ax^2+bx+c

Therefore, in this case, our a is -5, b is 40, and c is 45.

So, let's find the x-coordinate of our vertex. Substitute 40 for b and -5 for a. This yields:

x=\frac{-(40)}{2(-5)}

Multiply and reduce. So:

x=-40/-10=4

Now, substitute 4 for t to find the height. So:

-5(4)^2+40(4)+45

Evaluate:

=-5(16)+40(4)+45

Multiply and add:

=-80+160+45=125\text{ meters}

Therefore, the highest the rocket goes up is 125 meters.

Part 2)

To find out for how much time the rocket is in the air, we can think about after how many seconds after launch will the rocket land.

If the rocket lands, the height h will be 0. So, we can set our expression equal to 0 and solve for t:

-5t^2+40t+45=0

First, let's divide everything by -5. This yields:

t^2-8t-9=0

We can factor:

(t+1)(t-9)=0

Zero Product Property:

t+1=0\text{ or } t-9=0

Solve for t:

t=-1\text{ or } t=9

In this case, since t is our time in seconds, -1 seconds does not make sense. So, we can remove -1 from our solution set.

Therefore, 9 seconds after launch, the rocket will touch the ground.

Therefore, the rocket was in the air for 9 seconds.

And we're done!

You might be interested in
17.
IrinaVladis [17]

Answer:

$32 + $0.25x < $50

Step-by-step explanation:

1.he buy a backpack for $32

2. he buys x amount of pencils. Each pencil cost 0.25. ($0.25x)

3. all of that is less than(<) $50

4 0
2 years ago
Solve for x. Show all work. 2/3 (x+7) =10
Anna35 [415]

Answer:

answer is 8

Step-by-step explanation:

2/3(x+7)=10

2x/3+14/3=10

2x/3=10-14/3==>30-14/3

2x/3=16/3

x=16/3*3/2

x=8

7 0
3 years ago
4. A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the
Vitek1552 [10]

Answer:

  • C. 0.08889

Step-by-step explanation:

<u>Total number of marbles:</u>

  • 5 + 2 + 1 + 2 = 10

<u>There are two possibilities</u>

  • Orange then green or green the orange

<u>The probabilities are:</u>

  • P(o&g) = 2/10*2/9 = 2/45
  • P(g&o) =2/10*2/9 = 2/45

<u>Required probability is:</u>

  • P = 2/45*2 = 4/45 =  0.08889

Correct choice is C

4 0
2 years ago
Solve the one step inequality
drek231 [11]
Subtract -3-5 use Keep Change-Change
 keep -3
 change the - into a +
change 5 into -5
so... -3 + -5 is -8
-8 is the answer
7 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the points (−7,5) and (-7,-8).
Viefleur [7K]

Answer:

x = -7

Step-by-step explanation:

First we find the slope using

m = ( y2-y1)/(x2-x1)

   = ( -8 - 5)/( -7 - -7)

   = (-8-5)/(-7+7)

   = -13/0

This means the slope is undefined and the line is vertical

Vertical lines are in the form

x= constant and the constant is the x value of the points

x = -7

3 0
3 years ago
Other questions:
  • Identify the 34th term of the arithmetic sequence 2, 7, 12
    14·1 answer
  • Let f(x) = x ^ 2 and g(x) = x - 3 . Evaluate (g?f)(0).
    13·1 answer
  • Please answer will mark as brainliest
    8·2 answers
  • What is the length of AC
    12·2 answers
  • ANSWER FAST PLZ 65 POINTS!!!!!!!!!!!!!!!!!!
    12·2 answers
  • Transformations<br>I need help on this worksheet please.
    9·1 answer
  • Could someone help me with this? it'd be very appreciated!
    12·1 answer
  • Getaway Travel Agency surveyed a random sample of 45 of their clients about their vacation plans. Of the clients surveyed, 21 ex
    6·1 answer
  • Two shops sell baked beans in different sized tins. Calculate the price per 2.5 kg for shop B. Give your answer in pence. Write
    9·2 answers
  • Complex Numbers
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!