amazingxin777

From the picture we know that the diameter of the sphere is equal to the height and "width" of the cylinder. We know that a sphere's volume is \(\frac{4}{3}\pi r^3\) where \(r\) is the radius. We also know that the cylinder's volume is \(\pi r^2 h\) where \(r\) is the radius and \(h\) is the height. But as we said before (because the sphere is inscribed within the cylinder) that the height and "width" (diameter) is the same so we can rewrite that to \(2\pi r^3\). The ratio of it is \(\frac{\frac{4}{3}\pi r^3}{2\pi r^3}\). \(\pi r^3\) cancels out and we are left with \(\frac{\frac{4}{3}}{2}\) simplify that to \(\Rightarrow\) \(\frac{4}{2\times3} \Rightarrow \frac {4}{6}\) . We can simplify that further to \(\frac{2}{3}\) because both are divisible by 2. So the answer is \(\boxed{\frac{2}{3}}\) or \(\boxed{2:3}\)

nvm i figured out the question

the answer is \(\sqrt{2}\) and your hint was actually really helpful thx!

First we have to figure out what 1001011-100110. If you use a calculator (or if you use scratch paper) you get: 900901. Binary is basically base 2. If you know how to convert between base 10 and another base (in this case, it is base 2) this is a rather simple problem; it just takes a lottt of computing. If you compute (it does take a while) you get 11011011111100100101

plz post a question at a time 

gr8 ans!

First find the ones that are divisible by 3, then 4, then 5. Minus the repeats!

this was very clear! but you could add that there is a formula: \(a^2+2ab+b^2=(a+b)^2\)

you mean below diagram

HInt: If they are perpendicular, then their slopes are the negative reciprocrals of each other. 

There are a few issues:

#1: where are the boxes?

#2: please fix your LaTeX, i can't tell what that is