SOLUTION: A right triangle has a leg of length x and a hypotenuse of length 2x. Write an equation to find the length s of the other leg, and use it to estimate s when the hypotenuse has a l

Algebra ->  Rational-functions -> SOLUTION: A right triangle has a leg of length x and a hypotenuse of length 2x. Write an equation to find the length s of the other leg, and use it to estimate s when the hypotenuse has a l      Log On


   

Question 180607: A right triangle has a leg of length x and a hypotenuse of length 2x. Write an equation to find the length s of the other leg, and use it to estimate s when the hypotenuse has a length of 5 cm??



If ƒ(x) = 5x + 8, find (ƒ-1 ° ƒ)(59) and (ƒ ° ƒ-1)(3,001).
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
A right triangle has a leg of length x and a hypotenuse of length 2x. Write an equation to find the length s of the other leg, and use it to estimate s when the hypotenuse has a length of 5 cm??
:
1)s%5E2%2Bx%5E2=%282x%29%5E2
:
if hypothenuse is 5 then x=5/2
:
s%5E2%2B%285%2F2%29%5E2=5%5E2
:
s%5E2=25-25%2F4=75%2F4
:
s=sqrt%2875%2F4%29=sqrt%2825%2A3%2F4%29=%285%2F2%29%2Asqrt%283%29
:
:
2)If ƒ(x) = 5x + 8, find (ƒ-1 ° ƒ)(59) and (ƒ ° ƒ-1)(3,001).
:
f%5E-1 is x=5y+8--->5y=x-8--->y=(1/5)x-(8/5)
:
so f%5E-1=%281%2F5%29x-%288%2F5%29
:
for (ƒ-1 ° ƒ)(59)...we need to take the f(59) first and the f%5E1 of that result.
:
f%2859%29=5%2859%29%2B8=303
:
f%5E-1%28303%29=%281%2F5%29303-%288%2F5%29=295%2F5=59......so (ƒ-1 ° ƒ)(59)=59
:
for (ƒ ° ƒ-1)(3,001). we take the f%5E-1%283001%29first and then the f of that
:
result.
:
f%5E-1%283001%29=+%281%2F5%293001-%288%2F5%29=2993%2F5
:
f%282993%2F5%29=5%282993%2F5%29%2B8=2993%2B8=3001
:
Notice how we ended up with the same value as we started with????