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
Soloha48 [4]
2 years ago
5

A child lets go of a balloon that rises at a constant rate. 5 seconds after it was released, the balloon is at a height of 16 fe

et above the ground. After 20 seconds of rising, it is at a height of 52 feet above the ground. 1. Write a linear model for the height, h, of the balloon as a function of the number of seconds, s that it has been raising. 2. What was the height of the balloon initially before the child let it go? 3. Use your model to predict the height of the balloon after 90 seconds. Only an algebraic solution will receive credit.
Mathematics
1 answer:
Mama L [17]2 years ago
8 0

Answer:

1. h = 2.4t + 4

2. 4 feet

3. 220 feet

Step-by-step explanation:

1. Write a linear model for the height, h, of the balloon as a function of the number of seconds, s that it has been raising.

Since the balloon rises at a constant rate, we find this rate by using the initial and final values of height and time at 5 seconds and 20 seconds respectively which are 12 feet and 52 feet respectively.

So, rate = gradient of line

= change in height/change  in time

= (52 ft - 16 ft)/(20 s - 5 s)

= 36 ft/15 s

= 2.4 ft/s

Now the equation of the line which shows the height is gotten from

(h - h')/(t - t') = rate

Using h'= 16 feet and t' = 5 s, we have

(h - 16)/(t - 5) = 2.4

h - 16 = 2.4(t - 5)

h - 16 = 2.4t - 12

h = 2.4t - 12 + 16

h = 2.4t + 4

where h is the height of the balloon above the ground and t is the time spent in the air in seconds.

2. What was the height of the balloon initially before the child let it go?

We obtain the initial height of the balloon before the child let go at time, t = 0 the time before the child let go.

So, substituting t = 0 into the equation for h, we have

h = 2.4t + 4

h = 2.4(0) + 4

h = 0 + 4

h = 4 feet

So, the height of the balloon before the child let go is 4 feet above the ground.

3. Use your model to predict the height of the balloon after 90 seconds.

We insert t = 90 s into the equation for h. So,

h = 2.4t + 4

h = 2.4(90) + 4

h = 216 + 4

h = 220 feet

So, the height of the balloon after 90 s is 220 feet above the ground.

You might be interested in
Solve each system by elimination. -8x14y=-14. 5x+7y=0<br><br>help me solve this please.
katrin2010 [14]
The answer is (7/9, -5/9)

(7 over 9 and negative 5 over 9)
8 0
3 years ago
Read 2 more answers
A stack of six bricks is two feet high. How many bricks are in a stack of 20 feet high? How high is a stack of 20 bricks?
Flura [38]
I believe it is 7 feet high
5 0
3 years ago
Read 2 more answers
Which of these is not random?
Naily [24]

2nd one behsbshsnnshs

6 0
2 years ago
Two over twenty-two plus six over eleven
kirill [66]

\frac{2}{22}+\frac{6}{11}


Simplify \frac{2}{22} to \frac{1}{11}


\frac{1}{11}+\frac{6}{11}


Both are over 11, so, just sum.


\frac{1+6}{11}

\frac{7}{11}

4 0
3 years ago
Read 2 more answers
how many license plates can you make when a license plate consists of 6 out of 26 alphabetical letters each of which can be repe
UkoKoshka [18]
Idk if this is right bc it’s just a guess but maybe 156 bc that’s 26x6
4 0
3 years ago
Other questions:
  • You’re given three angle measurements of 30°, 70°, and 80°. How many triangles can you construct using these measurements?
    10·2 answers
  • Which is the correct answer?
    14·1 answer
  • MARKING BRAINLIEST, PLEASE HELP. <br><br> Find the value of x, show your work.
    7·2 answers
  • As per an axiom in Euclidean geometry, if points lie in a plane, the containing those points also lies in the same plane?
    15·2 answers
  • Someone answer this plz, ill be ur frend
    15·1 answer
  • 20 POINTS
    9·1 answer
  • I NEED AN EXPLANATION!!!
    7·1 answer
  • Kristina owns a local bakery and sells boxes of cannolis. Each box contains 9 cannolis. If she sells 6 boxes of cannolis by clos
    12·1 answer
  • 5<br> The slope of EF is<br> Which segments are perpendicular to EF?<br> Select each correct answer.
    5·1 answer
  • Finding the surface area
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!