# tough

1. ### Tough Geometry Course

What is the most challenging geometry course in the world of math?
2. ### Tough Inexact equation

I've been working on this inexact equation for a while and can't seem to finish it up properly. I get down to the last step where you have to solve for the "constant of integration" (which is a function of y), but when I isolate C'(y) I get x terms. The problem is \$ x^2 + 2xy + y^2 + (y^2 + 2xy...
3. ### Tough Limit

Hello, Am stuck at this one \displaystyle\lim_{x\to1} \sqrt{x-1} \cdot ln\left(ln\left(\frac{1}{x}\right)\right) Basically re-write it as \displaystyle\lim_{x\to1} \dfrac{ ln\left(ln\left(\frac{1}{x}\right)\right) }{ (x-1)^{\frac{-1}{2}} } and start applying L'Rule. But it never ends and...
4. ### Tough interest rate problem

My friend taking the GED has this problem and I am unable to help them: PV= P 1-(1+i)-n\ i Brian took 8 years to pay off his 71900 loan. Th eloan had an interest rate of 8.16% compounded quarterly. If Brain paid quarterly and made the same payment every time, how much was each payment that he...
5. ### Another tough Geometry Question ( Pythagoras and Circles and Tangents)

Hi guys, another tough problem thats giving me some trouble. I thought i might look to the geniuses on this forum for help. Anyway, i am attaching a picture, basically i have to find the radius of the circle using phythagoras. The smaller circle has a radius of 1cm and the angle between the...
6. ### Three tough problems.

Sorry for such vague title. Anyway, I am doing some math evaluation test when I ran across these bad boys. For question #1, I have no idea where to begin. For question #2, I forgot how to deal with absolute values. For question #3: y= x+1 So, y^2 = x^2 + 2x +1 Sub that into the other equation...
7. ### Tough series to test for convergence

Hello, Test the series for convergence from n=2 to n=infinity of 1 / ( ln(n) )^9 The whole ln is raised to power 9 Tried as much as I can and nothing comes out I believe it needs advanced tests not the basic ones.
8. ### Tough Trig Identity

cot(2x) = csc(2x) - tanx I tried working with either side, but I couldn't get anywhere. Any help is appreciated!!
9. ### Tough Connected Problem

I just need help understanding this problem: Suppose that \{X_i,\Omega_i) : i\in I\} is a family of topological spaces and suppose that \bold{x} and \bold{y} are members of \prod \{X_i : i\in I\}. If \bold{x} and \bold{y} differ in only one coordinate, prove that they must lie in the same...
10. ### Tough Algebraic question for a 10 year old

Here's the problem: If X horses can eat through Y bags of feed in Z days. How many days would U bags of feed last with V similar horses eating at the same rate? My answer: Let the number of days be a = U/V The rate of eating for each horse is Y/X per day V similar horses would...
11. ### Tough Probability Example

This question is hard to picture on paper. Could someone please help me visualize what is going on in this problem? Thanks in advance!! (The photo hase some issues and the textbook does not give a visual aid for this example. In a forest there are n trees per hectacre evenly spaced. The...
12. ### Tough geometry problem

Consider triangle ABC, BE and CF are medians. BE = 18. CF = 24 and BC = 20. Find perpendicular distance between A and BC.
13. ### rearrange tough equation

Hi, I am trying to rearrange the following equation to isolate V, but am having trouble working out the right strategy. Could someone help me by pointing me in the right direction? I have read about the Lambert W function and it seems like it might be suitable but don't know how to use it...
14. ### Tough Optimization Question

Can someone send me the full steps so i can learn from it, i missed the lecture today so i didn't get the step by step walk through of the solution :( i'm having such a hard time with the optimization unit it's really tough... and our textbooks only give us to answer so i have no idea how to...
15. ### Tough Physics Problem( grade 11)

This is a problem from my Kinematics unit and I am struggling to solve it: Two toboggans are connected by a rope. The first toboggan has a mass of 60kg and the second has a mass of 40kg. The two toboggans are pulled by a rope connected to the first toboggan.If the force exerted on the rope is...
16. ### Intergration and anti differentiation tough question

How do you make the area above a line enclosed by the curve equal to the area below a line enclosed by the curve. It is the same line running through the curve , x^3 - 14x^2 +59x - 70 , the line is mx -70, I need to find a value for m to make the area above the line enclosed by the curve...
17. ### Approximation Error and Tough Integral

Hello Everyone! Today We are asked to find \int_{1}^{2} e^\frac{1}{x}dx. We are given two option. First is by evaluating the definite integral itself or we can do numerical approximation using both Trapezoidal and Mid point Rules with sub interval n valued at 10. Since I've figured out that...
18. ### Tough linear algebra question

Let P11 be set of polynomials with degree <= 11, let S be its subspace of p11 givin a polynomial function f so that f(11)=f(10)=f(12), what is the dimension of S ?
19. ### a tough DE

Hello everyone, I haven't learnt very much about differential equations in school so far, but I came accross one I must solve for a physics project. I tried looking at the guides here in the forum but at a glance I don't see how they apply to my equation, and learning all the different...
20. ### Tough Differential Equation Problem

I need to find a function F such that it is continuous everywhere and y'(t)=F(y(t)) and y(0)=0 The only thing i could think of is y(t)=e^t but that obviously doesnt satisfy the initial value. Any help or hints is greatly appreciated.