math help-pre calc functions

[JonathanBelles]

1. find a formula that expresses that area A of an equilateral triangle as a function of the length S of a side.

2. Express the perimeter P of a square as a function of its area A.

3. Express the surface area S of a sphere as a function of its volume V.

[Derek Ortt]

1. S= length of a side
.5S^2 (just apply the triangle forumla, that one took about 2.5 seconds to figure out

3. A=dv/dr (it happens that the surface area is the derivative of the volume)
a=4*pi*r^2=(3*V)/r

[whereverwx]

Problem #49 on this website may help you with #2. In addition, also search the PDF for small words or phrases, since there are quite a few problems on there.

[JonathanBelles]

1. area of an equilateral triangle is ((root 3)s^2)/4
how is your answere a function>

im lost

[tropicana]

i wish i were a math wizard

[wxmann_91]

3. A=dv/dr (it happens that the surface area is the derivative of the volume)
a=4*pi*r^2=(3*V)/r

I don't think fact knows calc yet (he's in Precalc).

Anyhow...he's the algebra way to do it...I love MathType




EDIT: In retrospect, that may not be a function. I'll look over it again...

[wxmann_91]

1. S= length of a side
.5S^2 (just apply the triangle forumla, that one took about 2.5 seconds to figure out

#1 is incorrect. Base is different from height.

[JonathanBelles]

no i havent taken calc yet. i still dont get #1

[wxmann_91]

no i havent taken calc yet. i still dont get #1

What about it is confusing you, fact?

[JonathanBelles]

according to my pre calc book the area of an equilateral triangle is (root3*s^2)/4

[wxmann_91]

according to my pre calc book the area of an equilateral triangle is (root3*s^2)/4

Isn't that what I have? Change the b to an s and place the variable in the numerator.

[JonathanBelles]

so (root3*s^2)/4 is the answer?

[wxmann_91]

yes...that one's the easiest one.

Other two are a bit more tricky. Calamity's link has the second one, but for the third one, I'm not so sure I am right since that's not a function. I'm pretty sure the process has something to do with eliminating r. Maybe try solving both equations for r (w/o r in both sides) and then setting them equal to each other, finally simplifying.

[Derek Ortt]

strike what I said about one... major brain freeze, height is not the same as the base, use the 30/60/90 triangle relation to get the height in terms of the base

[Skyhawk]

2. For a square, the the length of a side is the square root of the area, s = A^1/2; therefore P = 4*(A^1/2)

3. Solve the volume formula for r, r = (3*V/4*Pi)^1/3. Then SA = 4*pi*r^2. Substitute for r and simplify.

Back in the "dark ages" when I went to school we didn't have such pretentious names for these courses such as precalculus. We just called it algebra, rather simple algebra at that.