SOLUTION: 19. The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions.  Then show how you use those solutions to find the two cons

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 19. The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions.  Then show how you use those solutions to find the two cons      Log On


   

Question 1155921: 19. The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions.  Then show how you use those solutions to find the two consecutive positive integers.
 
 
20. A cannon ball is shot from a cannon on top of a hill that is 73.5 meters above sea level. The cannon ball leaves the cannon with a velocity of 9.8 m/s. Write and solve a quadratic equation to determine when the cannon ball will reach sea level
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

19.
Let first integer be x
Let second integer be %28x%2B1%29
if their product is 42, we have
x%28x%2B1%29=42
x%5E2%2Bx=42
x%5E2%2Bx-42=0..factor
x%5E2%2B7x-6x-42=0
%28x%5E2%2B7x%29-%286x%2B42%29=0
x%28x%2B7%29-6%28x%2B7%29=0
%28x+-+6%29+%28x+%2B+7%29+=+0
=> solutions:
if %28x+-+6%29+=+0=>x=6
if +%28x+%2B+7%29+=+0=>x=-7-> disregard negative solution
so, the two consecutive positive integers are
x=6
x%2B1=7


20.
the projectile height is modeled by the equation
h=-16t%5E2%2Bvt%2Bs
and can be written using metric units as
h=-4.9t%5E2%2Bvt%2Bs where the units are converted from feet to meters
so, using

h=-4.9t%5E2%2Bvt%2Bs+ ...plug in given v=9.8+m%2Fs and s=73.5m,
h=-4.9t%5E2%2B9.8t%2B73.5+
when the cannon ball reach sea level,+h=0
so,
0+=+-4.9t%5E2+%2B+9.8t+%2B+73.5
0+=+-4.9%28t%5E2+-+2t+-+15%29
0+=+-4.9%28t+-+5%29%28t+%2B+3%29
solutions:
if t+-+5+=+0 =>t=5
if t+%2B+3+=+0=>t=-3
your solution will be:
t+=+5+since+t+=+-3 is not acceptable negative value
Hence, the cannon ball will reach sea level at+5+seconds.