Question 817600: A duck drives under water and its path is describe by the equation y= 2x^2 - 4x, where y represent position of duck in meters and x represent time in seconds.
a) how long was the duck under water?
b) how long was the duck under water at least 0.5 meters below water surface?
- thank you.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! y = 2x^2 - 4x
---
part a:
---
0 = 2x^2 - 4x
---
the above quadratic equation is in standard form, with a=2, b=-4, and c=0
---
to solve the quadratic equation, plug this:
2 -4 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
the roots of the quadratic are:
x = 2
x = 0
---
Answer a:
the duck was underwater (y <= 0 meter ) for 2 seconds
---
part b:
---
0.5 = 2x^2 - 4x
0 = 2x^2 - 4x - 0.5
---
the above quadratic equation is in standard form, with a=2, b=-4, and c=0.5
---
to solve the quadratic equation, plug this:
2 -4 0.5
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
the roots of the quadratic are:
x = 0.133974596
x = 1.8660254
---
Answer b:
dt = 1.8660254 - 0.133974596 = 1.7320509
the duck was underwater below half a meter depth (y <= 0.5 meter ) for 1.73 seconds
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
|
|
|
