Recent content by Mr Davis 97

Sorry, ##a = \operatorname{dim} V## and ##b = \operatorname{dim} W##. And yeah, I actually did that and I think I was able to solve it in that case. Basically, if we're trying to find the dimension of ##\{ T\in \mathrm{Hom}(V,W) : T(v_1) = 0 \}##, where ##v_1## is nonzero, then if we define...

But I guess what I'm saying is that wouldn't this problem restrict itself to the interval ##[0.5, 5]## because that's all we're given?

All we're given is that y = f(x). We don't know what kind of function it is. And it probably isn't ##-\infty## because that seems too complex for the nature of the question.

This seems like a simple problem, but I am a little confused by a few things. For one, what is the use of the piece of information that when they charged $100 per person they got 3000 people to come? Also, how should I proceed with the information "for every $2 decrease in price they would have...

Any hints? I feel for someones who knows topology this would be an easy problem

A line in this case is a segment from one side of the quadrilateral to the other. Here is the problem I am actually trying to solve: Let ##Q## be a convex quadrilateral which is cut into convex pieces (cells) by a finite number of lines. For any collection ##(Q_i)_1^n## of these cells...

I can construct examples that are less than or equal to ##4n## quite easily, but for the life of me I cannot come with example where it's greater than

A convex disc is any compact, convex set with non-empty interior

So as someone who has a limited understanding of topology, what would be a hint or a first step for this?

Here is the problem: Let ##C## be a convex disc in the plane, and ##C_1## and ##C_2## be two translates of ##C##. Prove that ##C_1## and ##C_2## are non-crossing, that is, it isn't possible that both ##C_1 - C_2## and ##C_2 - C_1## are non-connected. Here is my question: What exactly do the...

This is a pretty simple question, I am just trying to clear up confusion. Let ##D## be the rectangle in the plane with vertices ##(-1,0),(-1,1),(1,1),(1,0)##. Let ##\lambda >0##. Then what exactly does the set ##\lambda D## look like? Is it correct to say that, for example, ##2D## is the...

Suppose ##t \ge 0##. Let ##\displaystyle I(t) = \int_{-\infty}^{\infty}\frac{x \sin (tx)}{x^2+1}~\text{dx}##. Call this form 1. Note that we can also write the integral as $$ \begin{align*} I(t) &= \int_{-\infty}^{\infty}\frac{x \sin (tx)}{x^2+1}~\text{dx} \\ &=...

Problem: Let ##L## be a set of ##n## lines in the plane in general position, that is, no three of them containing the same point. The lines of ##L## cut the plane into ##k## regions. Prove by induction on ##n## that this subdivision of the plane has ##\binom{n}{2}## vertices, ##n^2## edges, and...