How do I derive the volume of this cup? It's been many years since I've taken calculus... So far I've started with the radius of the bottom...

I am to solve $5\log_7(n)=10$. I arrived at $n=7^5$ while the solution in my textbook says it's $49$ My working: $$5\log_7(n)=10$$ $$\log_7(n^5)=10$$...

Now this question might sound a bit weird to some people, but the situation is this: Say I have the number $0.999..$ where there is an infinite number of ...

As in the question I completed the first part by a substituion of $x=a\sin(t)$ after which the answer was easy to obtain. With regards to the second part ...

I've been working through "Groups and Symmetry" (Armstrong) and came across this problem in chapter 9 which I can't figure out. Any hints/help w...

I am looking for a easy way for dividing a regular hexagon into 5 equal parts and preferably equal shapes or continuing shapes to make it easy to see the ...

I have this 3D Triangle of which I want to get the interpolated normal of V3. I know how to get the normal per triangle face, but I don't know how to...

The question is given in the chap. 1.4 of the book titled: Calculus Problems for the new century, by Robert Fraga. What is the domain of $\operatorname{ar...

$\cos^2 x = 1$ How do you solve trig equations with a power? Unsure what to do with the square? I get this $\frac{1+\cos2x}2 =1$ $\cos2x =1$ $2x=2n\pi\pm0...

Or, in general, what does the magnitude of the cross product mean? How would you prove or disprove this?