Math

[JaeSon15]

Actually, the set of numbers between 1 and 2 has the same size as those between 1 and 3. The proposition which was crazy back then, though fairly accepted today, was that a line segment can be put into correspondence with a square.

So really when you're dealing with infinite sets, there are only two sizes: countably infinite and uncountably infinite.

So, here's another counterintuitive example: The set of natural numbers has cardinality equal to the set of integers. This almost doesn't make sense, but here's one particular correspondence: (1,0), (2, -1), (3, 1), (4, -2), (5, 2), (6,-3), (7, 3), ...

[katya]

I think you're going to have to explain that a little better.

Originally Posted by trolls' bane

I wonder if Achilles has passed the tortoise in the race yet...

LOL Last I hear he hasn't moved. I'm sure he'll comel through though. Good ol' Achilles.

[shesabrandybuck]

Help?! Problem:

You are currently hiking up a mountain. The distance that you have hiked from your car, C, to the bottom of the moutain, M, is 2km. You began climbing the mountain and have been climbing uphill for 7.2km. According to your very detailed contour map, you know that the mountain is at an angle of 30 degrees to the ground below. Find the distance from your car to you, Y, at this point.

I believe that you would use Law of Cosines: a^2=b^2+c^2-2bc*cos(A)

[sisterandcousinandaunt]

Well, I'd just use geometry, so I'm no help.

[shesabrandybuck]

If I did geometry then I would have to break the triangle into two right triangles, and I dont have enough information to do that
*curses trig*

[sisterandcousinandaunt]

check the teacup.

[Ilfirin]

Wow! A thread for Math too!

Miss Brandybuck, you're absolutely right abt using the cosine rule. Lets call the trianlge YMC(Y is where the person is at some point on the mountain, M is the bottom of the Mountain, C is the car.) It is an obtuse angled triangle. They've given (angle)YMC, which is an exterior angle,30 deg. Hence inside the triangle, (angle) YMC is 150 deg. MC is 2km and YM is 7.2 km.

So by Cos rule YC = sqrt( YM^2 + MC^2 - 2(YM)(MC)cos 150)

Approx 8.99 km.

It can also be solved by breaking it up into two triangles(right angled).

Ilfirin

P.S: Now my MS Paint skills are quite bad, so could not help with an actual diagram.

[shesabrandybuck]

I tried to make a diagram on paint, but it wouldnt upload.
I turned the paper in today with that problem, and I forget what I got as my answer, but I think it just might have been that, I'll let you know

[Count Comfect]

Originally Posted by JaeSon15

Actually, the set of numbers between 1 and 2 has the same size as those between 1 and 3. The proposition which was crazy back then, though fairly accepted today, was that a line segment can be put into correspondence with a square.

So really when you're dealing with infinite sets, there are only two sizes: countably infinite and uncountably infinite.

Not technically true. Georg Cantor would have told you that there are infinite infinities (example - 2^c, where c is the infinity corresponding to the number of real numbers, is another infinity beyond c itself). Aleph-null (countable infinity) and c are just the easiest to grasp.

[shesabrandybuck]

In a poll, 35 people were in favor of building a new library, 14 people were against it, and 1 person had no opinion. What fraction of those polled were in favor of building a new library?

I got 7/10, but the answer is 2/3...help!



edit: I am so retarded, I've been looking at the answers wrong, I was right, it is 7/10. My bad

[Count Comfect]

Originally Posted by shesabrandybuck

In a poll, 35 people were in favor of building a new library, 14 people were against it, and 1 person had no opinion. What fraction of those polled were in favor of building a new library?

I got 7/10, but the answer is 2/3...help!



edit: I am so retarded, I've been looking at the answers wrong, I was right, it is 7/10. My bad

Easiest way to get a math problem wrong: read the answer wrong

[shesabrandybuck]

A container manufacturer must make a rectangular box with a volume of 500 cubic centimeters. The end of the box must be twice as wide as it is high. Let x be the height of the box.

a. Express the length l of the box as a function of x.
b. Write a function that gives the surface area S of the closed box as a function of x.
c. Use a graph to estimate the height that produces the minimum surface area.



So lost, does anyone know?

[Count Comfect]

Volume of box = width * length * height.

width = twice height; height defined as "x"
width = 2x

Volume = 2x*l*x = 500 cm^3 2x^2*l=500 l=500/(2x^2)

Surface area = the area of all 6 sides (top and bottom, 2 ends, left and right sides)

= 2* (width*length) + 2*(length * height)+ 2*(height*width) = 2*(2x*(500/2x^2))+2*((500/2x^2)*x)+2*(2x*x) = 2*(500/x+500/2x+2x^2) = 2*(1000+500+4x^3)/(2x) = (1000+500+4x^3)/x

[shesabrandybuck]

Hey, thanks so much! But, I figured it out...
But still, thanks a lot for helping