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
Marina CMI [18]
2 years ago
11

Micah is writing a function that models the height a dolphin reaches when it propels itself from underwater to the surface, leap

s through the air, and reenters the water. The model is represented by the equation h=-16t+96t-128, where h is the height in feet above the surface of the water and t is the time in seconds. According to Micha's model, how long will the dolphin be above the surface of the water?
Mathematics
1 answer:
stepladder [879]2 years ago
4 0

Answer:

The dolphin will be above the surface of the water for 2 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

The height of the dolphin after t seconds is given by:

h(t) = -16t^2 + 96t - 128

According to Micha's model, how long will the dolphin be above the surface of the water?

It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which h(t) = 0 it crosses the surface upwards, and then the second time for which h(t) = 0 it crosses the surface downwards.

We have to find these roots. So

h(t) = -16t^2 + 96t - 128

-16t^2 + 96t - 128 = 0

Multiplying by -16

t^2 - 6t + 8 = 0

\Delta = (-6)^{2} - 4*1*8 = 36 - 32 = 4

t_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4

t_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2

4 - 2 = 2

The dolphin will be above the surface of the water for 2 seconds.

You might be interested in
Compare the wins-to-losses ratios for the teams. Team Records Team Wins Losses Cougars 12 10 Bobcats 20 10 Bulldogs 8 5 Tigers 3
UkoKoshka [18]

Answer:

Bobcats

Step-by-step explanation:

The wins-to-losses ratio for the Cougars is 12:10.  This can also be written as 12/10; writing this as a decimal, we would have 1.2.

The wins-to-losses ratio for the Bobcats is 20:10.  This can also be written as 20/10, which is the same as 2.0.

The wins-to-losses ratio for the Bulldogs is 8:5.  This can also be written as 8/5, which is the same as 1.6.

The wins-to-losses ratio for the Tigers is 3:5.  This can also be written as 3/5,l which is the same as 0.6.

The largest of these decimals is 2.0; this means the Bobcats have the greatest ratio of wins to losses.

4 0
3 years ago
Read 2 more answers
The sales tax in New York City is 4%. which expression can be used to find The amount of sales tax on a $50 Item?
ahrayia [7]
<span>4/100×50 is your answer $2</span>
5 0
2 years ago
which statement is true about the equation 3/4z-1/4z+3=2/4z+5. It has no solution. It has one solution. It has two solutions. It
kozerog [31]
3/4z - 1/4z + 3 = 2/4z + 5
3/4z - 1/4z - 2/4z = 5 - 3
2/4z - 2/4z = 2
0 ≠ 2
----------------------------
<span>It has no solution.</span>
3 0
3 years ago
Read 2 more answers
Use the number line to find (One-fourth) + (negative StartFraction 21 over 8 EndFraction) Negative StartFraction 19 over 4 EndFr
Shalnov [3]

Answer:

-\frac{19}{8}

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A football stadium has 2,500 seats. For the first game of the season, 2,075 seats were filled. Which percent of seats were fille
malfutka [58]
83 % of the seats

2075 / 2500 x 100
5 0
2 years ago
Read 2 more answers
Other questions:
  • Ellen has property whose boundary lines form a triangle, as shown in the diagram. Her house lies at Vertex A and she is going to
    12·1 answer
  • Find the surface area of the prism.
    15·1 answer
  • John Hikes 13.5 mi at a constant rate of 3 mi/ h
    9·2 answers
  • Find the average rate of change of a function that contains the points (-2,3) and (2,5).
    6·1 answer
  • Cassidy purchases a soccer ball that is regularly priced at $27.50. It is on sale for 30% off. What is the sale price of the soc
    9·1 answer
  • Forbes reports that women trust recommendations from Pinterest more than recommendations from any other social network platform
    15·1 answer
  • Sara needs 40 inches of yarn to glue onto each of 25 picture frames. She has a ball of yarn with a total of 950 inches. Which of
    14·2 answers
  • John runs a computer software store. Yesterday he counted 125 people who walked by the store, 66 of whom came into the store. Of
    9·1 answer
  • Use a table to multiply (-3a2)(a - b).
    9·1 answer
  • Owen’s rectangular garden has a length of (x+3) feet and a width of (x−4) feet. If the area of the garden is 18 square feet, wha
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!