Heave motion of a point energy absorber in the form of a buoy due t incident wave of frequency $w$ and amplitude $a$ is described by $(m+m_a)y''...

From what I've seen, ordered pair multiplication is $(a,b) \times (c,d) = (ac-bd,ad+bc)$. Also, $(0,1)$ represents $i$. So if I wanted to take $(0,-1...

I apologize if this is a duplicate of another question in advance. I did not find any in the search. Does $\sin(x)\sin(y)=\sin(xy)$? I am wondering becaus...

If you add the decimal digits of multiples of 9,possibly repeatedly, you get 9. For instance, with 18 we have $$18\mapsto 1+8=9$$ and with 909 we have $$ ...

In terms of $n$, how many distinct digraphs are there whose vertex set is $X$, where $X$ is a nonempty finite set with $|X| = n$? How does the answer chan...

The distances between the dots in the figure are equal to 1, both horizontally and vertically. What is the measure of the common area of the triangle and ...

I never understand what the trigonometric function sine is.. We had a table that has values of sine for different angles, we by hearted it and applied to ...

Prove that $\lim ((2n)^\frac{1}{n}) = 1$. I have obtained the following: $$(2n)^\frac{1}{n} = 1 + k_{n}; n > 1$$ $$(2n) = (1 + k_{n})^n$$ By the Binomi...

The instructions: Use the definition of derivative to find $f'(x)$ if $f(x)=\tan^2(x)$. I've been working on this problem, trying every way I ca...

Do I have to find out every element in D5 and draw a table to find out subgroups? I know how to find out every single element in D5, but can't think ...