Recent content by gex

Thank you so much Ray! I don't know how that didn't cross my mind. I successfully solved the problem now.

The Question: Attempt at a solution: I know for a fact that my attempt is fully wrong, but I am just grasping at straws here and have no clue how to approach this problem. Any help getting me to wrap my head around how to approach this is much appreciated. Thank you in advance.

Your equation is much cleaner than what I got and yields a root of m=1. Thank you so much for your help Charles, I will keep playing with the algebra in mine until it resembles your equation.

That is what I'm finding very difficult right now. I've been trying to solve for m myself but can't seem to do it. I used an online calculator and the provided root isn't an integer which leads me to believe I've gone wrong somewhere else in my algebra.

Thank you for your responses fresh_42 and Charles. I did what you suggested and came up with this. I'm unsure as to how to use this information to make my integrals definite.

Homework Statement The Attempt at a Solution The above is my attempt after playing around with the question for about an hour. I don't seem to know how to eliminate either Δy or b in order to solve for m. Any help is much appreciated. Thanks in advance.

Thank you for your help Mark, I finally solved the problem :)

The area for such a rectangle would equal 1/k. Substituting 1=k shows me that the area for the rectangle is larger than the region underneath the curve. Which makes sense as this shows that g(n) > f(n). But how would I go about proving this for all values of k ∈ Z ?

I'm really not sure how I would go about doing that, I've never encountered such a thing before in my studies. Sorry but I'm not quite sure what that is. My teacher provided a hint for this question to the class that I don't understand either, and I'm not sure where this hint is supposed to...

The above picture displays the graphs of f(n) and g(n) generated by https://www.desmos.com/calculator I understand what you mean by thinking about f(n) as an area underneath a graph, but am quite unsure how g(n) represents the sum of areas of rectangles. I would appreciate some clarification...

Homework Statement The attempt at a solution Hi there, in an attempt to prove that g(n) is greater than f(n), I graphed both functions on the same axes and it is visually obvious that g(n) is greater than f(n), but I am not sure how I would go about proving this for all positive integers in a...

Thank you so much everyone, I feel foolish for my careless sign error. Most of all I feel relieved that my approach wasn't flawed. I get the correct answer now :)

Mentor note: Thread moved from technical section, so missing the homework template. Hi all, I have a homework problem which asks me to compute the complex number cos(π/4 + π/4 i). I've been playing around with it for a while now and just can't seem to get the answer I get when using Wolfram...

Wow odd. I will ask the teacher about the provided answer being incorrect then, thank you for shedding some light on this haruspex.

Homework Statement A uniform, spherical cloud of interstellar gas has mass 2.03×1030 kg and radius 1.03x1013m and is rotating with period 1.43×106 years. The cloud collapses to from a star 7.03x108m in radius. Find the star's rotation period. Homework Equations I1ω1=I2ω2 Θ=ωt The Attempt at a...