# Thread: Applications of Functions :-)

1. ## Applications of Functions :-)

I have a couple of problems to check over for correction. I'm either over-complicating or over-simplifying them, ahahaha...

Please consider these... They're probably really easy...

Thank you!

(*) A rectangle has an area of 38 square feet. Determine the perimeter as a function of the length l.

(*) The volume of a right circular cylinder is 540 cubic centimeters. Express the height of the cylinder as a function of its radius r.

(*) The hypotenuse of a right triangle is twice as long as the height. Determine the height as a function of the base b.

2. Hey, that is true. In Math, we either over-simplify or over-complicate things. And if we get it just right enough, we were just lucky.

But then, who are to say what we did was just right enough?

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(*) A rectangle has an area of 38 square feet. Determine the perimeter as a function of the length l.

Rectangle.
width = w
length = L
Perimeter = w+L+w+L = 2w +2L = 2(w+L)
Area = w*L = wL

wL = 38
w = 38/L
Substitute that into the Perimeter,
Perimeter = 2(38/L +L) -------***
Over-simpliying that,
P = (76/L +2L)
P = (76 +2L^2)/L ----------****

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(*) The volume of a right circular cylinder is 540 cubic centimeters. Express the height of the cylinder as a function of its radius r.

Right circular cylinder.
Height = h
Volume = pi(r^2)h

pi(r^2)h = 540
h = 540 / pi(r^2) ----------***

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(*) The hypotenuse of a right triangle is twice as long as the height. Determine the height as a function of the base b.

Right triangle.
Base = b
Height = h
Hypotenuse = r

Given:
r = 2*h

By Pythagorean theorem,
r^2 = b^2 +h^2
Substitute 2h for r,
(2h)^2 = b^2 +h^2
4h^2 = b^2 +h^2
4h^2 -h^2 = b^2
3h^2 = b^2
h^2 = (b^2)/3
Get the square roots of both sides,
h = b / sqrt(3) ----------------------***
Over-simplifying that,
Rationalize the denominator,
Multiply both numerator and denominator by sqrt(3),
h = b*sqrt(3) / 3
h = (1/3)b*sqrt(3) ----------***

3. ## AH! Cool!

Yay, I'm happy... Thank you. I actually got the same answers... Woo-hoo!