SOLUTION: A rocket is fired upward from the ground with an initial velocity of 80 feet per second. The polynomial 80x-16^2 describes the height of the rocket, in feet, after x seconds. a) F

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rocket is fired upward from the ground with an initial velocity of 80 feet per second. The polynomial 80x-16^2 describes the height of the rocket, in feet, after x seconds. a) F      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 5799: A rocket is fired upward from the ground with an initial velocity of 80 feet per second. The polynomial 80x-16^2 describes the height of the rocket, in feet, after x seconds.
a) Find the rocket's height after 4 seconds
b) Factor the polynomial
c) Use the factored form of the polynomial in part (b) to find the rocket's height after 4 seconds. Do you get the same answer as you did in part (a)?
Answer by ichudov(499) About Me  (Show Source):
You can put this solution on YOUR website!
You surely meant 80x-16x%5E2, right?
For height at 4 seconds, use "4" instead of "x":
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: 80%2A4-16%2A4%5E2 simplifies to 64
  • Text form: 80*4-16*4^2 simplifies to 64
  • Cartoon (animation) form: simplify_cartoon%28+80%2A4-16%2A4%5E2+%29
    For tutors: simplify_cartoon( 80*4-16*4^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+80+%29%2Ahighlight_red%28+4+%29-16%2A4%5E2.
Multiplied numerator integers
It becomes highlight_green%28+320+%29-16%2A4%5E2.
Look at 320-16%2Ahighlight_red%28+4+%29%5Ehighlight_red%28+2+%29.
Replace constants in factor: highlight_red%28+4+%29,highlight_red%28+2+%29 with highlight_green%28+16+%29
It becomes 320-16%2Ahighlight_green%28+16+%29.
Look at highlight_red%28+320+%29-highlight_red%28+16%2A16+%29.
Replace constants in expression: highlight_red%28+320+%29,highlight_red%28+-16%2A16+%29 with highlight_green%28+64+%29
It becomes highlight_green%28+64+%29.
Result: 64

Universal Simplifier and Solver


Done!


so, 64 is the height at 4 seconds.
To factor, I use my quadratic solver:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B80x%2B0+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2880%29%5E2-4%2A-16%2A0=6400.

Discriminant d=6400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-80%2B-sqrt%28+6400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2880%29%2Bsqrt%28+6400+%29%29%2F2%5C-16+=+-0
x%5B2%5D+=+%28-%2880%29-sqrt%28+6400+%29%29%2F2%5C-16+=+5

Quadratic expression -16x%5E2%2B80x%2B0 can be factored:
-16x%5E2%2B80x%2B0+=+-16%28x--0%29%2A%28x-5%29
Again, the answer is: -0, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B80%2Ax%2B0+%29


factoring is -16x*(x-5).
If you again use 4 instead of x:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: -16%2A4%2A%284-5%29 simplifies to 64
  • Text form: -16*4*(4-5) simplifies to 64
  • Cartoon (animation) form: simplify_cartoon%28+-16%2A4%2A%284-5%29+%29
    For tutors: simplify_cartoon( -16*4*(4-5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+16+%29%2Ahighlight_red%28+4+%29%2A%284-5%29.
Multiplied numerator integers
It becomes -highlight_green%28+64+%29%2A%284-5%29.
Look at -highlight_red%28+64%2A%284-5%29+%29.
Removed extra sign in front of 64
It becomes highlight_green%28+64+%29.
Result: 64

Universal Simplifier and Solver


Done!


so, the answer is again 64!