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]
3 years ago
5

Super Dave Osborne stands at the bottom of a canyon elevation 256 feet below sea level, he throws a piano up at a velocity of 3

20 feet per second the piano lands on the edge of the cliff at zero elevation . The flight of the piano is modeled by the equation f( x ) = −16t2 2 + 320t − 256. The piano was in the air for exactly how many seconds
Mathematics
1 answer:
fgiga [73]3 years ago
6 0

Answer:

The piano was in the air for 18.34 seconds.

Step-by-step explanation:

The height of the piano after t seconds is given by the following equation:

f(t) = -16t^{2} + 320t - 256

Initially, the piano is below the ground level. At the first root of the equation, it will go into the air, and then some time after that it will fall down again, which is at the second root of the equation.

Roots of 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{\bigtriangleup}}{2*a}

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

\bigtriangleup = b^{2} - 4ac

In this question:

f(t) = -16t^{2} + 320t - 256

So

a = -16, b = 320, c = -256

\bigtriangleup = (320)^{2} - 4*(-16)*(-256) = 86016

t_{1} = \frac{-320 + \sqrt{86016}}{2*(-16)} = 0.8348

t_{2} = \frac{-320 - \sqrt{86016}}{2*(-16)} = 19.17

Subtracting:

19.17 - 0.8348 = 18.34

The piano was in the air for 18.34 seconds.

You might be interested in
A bank quotes an interest rate as 0.06341 annual effective yield. What interest rate, compounded monthly, will provide that
Leviafan [203]

9514 1404 393

Answer:

  0.06164

Step-by-step explanation:

The effective annual rate obtained by compounding nominal annual rate r monthly is ...

  eff rate = (1 +r/12)^12 -1

Then the value of r is ...

  r = 12×((eff rate) +1)^(1/12) -1)

For the given effective rate, that is ...

  r = 12×(1.06341^(1/12) -1) ≈ 0.06164 . . . . nominal annual interest rate

4 0
3 years ago
Someone please help me !
Greeley [361]
(2,5) I think I’m sorry if I’m wrong:/
5 0
3 years ago
Marsha counted 24 birds at the wildlife refuge, and Aamir counted 86 birds. What is the ratio of Aamir’s Burge to Marshall’s bir
vaieri [72.5K]

Answer:

43:12

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Helllohello help please if you want -
IRINA_888 [86]

Hey Hey! It's me again!

Answer:

The variable u divided by the variable x.

8 0
3 years ago
X2+6/5x+8/25<br> please help me.
Dmitriy789 [7]
The answer to your question is:

x^2 + 6/5x + 8/25;
4 0
3 years ago
Other questions:
  • The sum of four times a number and eight is between zero and twelve
    14·2 answers
  • Which of the following similarity statements about the triangles in the figure is true?
    12·1 answer
  • I need help with question 3
    5·1 answer
  • In three years, you want to travel to Europe which you expect to cost $10,000 at that time. You have deposited $5,000 in a Certi
    8·1 answer
  • Nolan surveyed 350 students at his middle school. Pizza was the favorite lunch of 42% of the students. How many students chose p
    10·1 answer
  • A hobby shop sells small and large toy cars. A small toy car is $5.50, and a large toy car is $9. What is an equation that relat
    5·1 answer
  • Stephanie claims that 26540is greater than 50. Do you agree or disagree? Explain.
    7·2 answers
  • A salesperson will earn a commission equal to 1/32 of the total sales. what is the commissions earned on the sales totaling 2400
    8·1 answer
  • WHOEVER ANSWERS THIS CORRECTLY I'LL GIVE BRAINLIEST!!!!!!!!!!!!
    9·2 answers
  • Please answer question
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!