Amy's Thread--Math

[King Bowzer]

ok amy your first question is this (i found it on the internet but i'm modifying it so it's not the same question: http://www.math.purdue.edu/academic/.../159E1-S06.pdf)

The rate at which a tablet of vitamin C dissolves depends on the surface area of the tablet. One brand of tablet is 2 centimeters long and is in the shape of a cylinder with hemispheres of diameter 0.5 centimeters attached to both ends, as shown in the figure. A second brand of tablet is to be manufactured in the shape of a right circular cylinder of altitude 0.5 centimeters.

a.) Find the diameter of the second tablet so that its surface area is equal to that of the first tablet.

b.) Find the volume of each tablet.

[Fearless™]

rofl. i forgot the formula for the sphere (actually i never knew it, so i had to google it Lol hopefully i used the right one =P)

uhh, diameter = 1 cm (the second pill thing)

volume of 2nd one = pi/8

1st one uhh: (3pi/32)+pi/6

dunno if it's right..i rushed through it cuz i need to study for my test tomorrow.

and that link u posted doesn't work lol.

[King Bowzer]

The link works for me. Does your browser support pdf files? Do you have Adobe reader installed? Anyway let's see..

Everything looks good except your volume for the first pill is off a little.

3pi/32+pi/6 evaluates to (18pi + 32pi)/(32*6) = 50pi/192 = 25pi/96

Let me run through the math real quick.

Volume of sphere = 4/3 πr³
Volume of cylinder = πr²h (h being the height/length of the cylinder)

Radius of hemispheres = 1/2 (0.5 cm) = 0.25 cm

Volume of spherical part of pill = 4/3 π(0.25)³ = π/48 cm³
Volume of cylindrical part of pill = π(0.25)²(2 - 0.5) = 3π/32 cm³

Add them together: π/48 + 3π/32 = (32π + 144π)/(48*32) = 176π/1536 = 11π/96 cm³

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Ok, the next problem will be more theory and less praxis.

Imagine a triangle. The vertices are A(8, 5), B(1, -2) and C(-3, 2). Tell me what kind of triangle ABC is and tell me its area.

Edit: Eh, I'll just tell you that it's a right triangle. But I'll ask you to prove it.

[The Girl From Ipanema]

Originally Posted by King Bowzer

The link works for me. Does your browser support pdf files? Do you have Adobe reader installed? Anyway let's see..

Everything looks good except your volume for the first pill is off a little.

3pi/32+pi/6 evaluates to (18pi + 32pi)/(32*6) = 50pi/192 = 25pi/96

Let me run through the math real quick.

Volume of sphere = 4/3 πr³
Volume of cylinder = πr²h (h being the height/length of the cylinder)

Radius of hemispheres = 1/2 (0.5 cm) = 0.25 cm

Volume of spherical part of pill = 4/3 π(0.25)³ = π/48 cm³
Volume of cylindrical part of pill = π(0.25)²(2 - 0.5) = 3π/32 cm³

Add them together: π/48 + 3π/32 = (32π + 144π)/(48*32) = 176π/1536 = 11π/96 cm³

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Ok, the next problem will be more theory and less praxis.

Imagine a triangle. The vertices are A(8, 5), B(1, -2) and C(-3, 2). Tell me what kind of triangle ABC is and tell me its area.

Edit: Eh, I'll just tell you that it's a right triangle. But I'll ask you to prove it.

I haven't done this stuff since highschool, but you have to prove that BC is perpencidular to AB in order to prove that its a right angle triangle right? And you do that by using those distance and midpoint and slope formulas right?

I love this stuff. .....I should take math again, but the next up math class would be like multivariable calculus or differential equations or some random hard core math class LOL...because the last class I took was calculus and Im pretty sure anything beyond that I could not stand a chance at passing

[Fearless™]

i still get 24 hrs right? cuz i'll do it tomorrow...when i've got a free period in class.

[King Bowzer]

Sure, I'll start the 24 hour timer...now. =)

[Cereal-Killa]

What has this got to do with science... or technology?

[Fearless™]

nothing (:

and rofl it literally took me 20 sec.

gradient of AB = 7/7 = 1

gradient of BC = 4/-4 = -1

multiply the 2 >> you get -1 so therefore the 2 likes are perpendicular and therefore it's a right angled triangle...

for the area, use the distance formula to get the length..then use pythagoras

AB = Root(98)
BC = root (32)

so area = 1/2*AB*BC

amiright? (:

[Fearless™]

oh and the link didn't work..prolly because i'm on dial up Lol so it takes ages for the stuff to load.

[King Bowzer]

Hey, good job. Are the questions too easy for you? Here's a different kind of question that involves composite functions. To refresh your memory, I'll briefly describe what a composite function is and how to find its domain. I'm assuming you have a little background in function theory. I'm also assuming the domain and ranges of all functions are subsets of R (all real numbers).

Take a function, f. Define f(x) to be x^2.
Take a function, g. Define g(x) to be 3x - 5.

The composite form f(g(x)) (sometimes denoted (f ○ g)(x)) is a function that takes g(x) and returns f(g(x)).

For example (f ○ g)(x) in this case:

f(x) = x^2
g(x) = 3x - 5
f(g(x)) = (3x - 5)^2.

The domain of (f ○ g)(x) is all x values in the domain of g such that g(x) is in the domain of f.

Here's your problem:

f(x) = x / (x - 2)
g(x) = 3/x

Find (f ○ g)(x), (g ○ f)(x), and the domain of g ○ f.