# hard

1. ### Riemanns Sum Problem

The Question: What I have so far: I have also proven that the vertical cross-sections result in the same formulae for Volume: The Questions: State one assumption that must be made and its associated effect in relation to finding a formula for the lightweight ‘pop-up’ tent. If the safety...

x+y+z=1 x^2+y^2+z^2=2 x^3+y^3+z^3=3 x^4+y^4+z^4=? answer is not 4 :) thanks.
3. ### a hard pentagon questionABCDE

ABCDE is a regular pentagon.CF is perpendicular to AB. KL is perpendicular to AC. |FB|=|KL|.|DE|=6 units. Find area of triangle AKC? https://postimg.org/image/8yw954k9z/ Question and image are very clear. I don't want any solution with trigonometry and golden ratio. I don't want to hear any...
4. ### Hard Problem (not sure which topic)

Problem -- "Let k and w be positive integers. If k is reduced by the sum of k's digits, the result is w. If w is increased by the sum of w's digits, the result is k + 2. Find the sum of the seven largest distinct possible three-digit values of k." Answer key -- 6592 My answer -- Ok, so I think...
5. ### Hard Geometry Exercise. Need Help !

In an orthogonal plane space, we consider the hyperbola I of equation xy=a, where a>0 1) Let be M1, M2, M3 three points I which abscissa are respectively x1, x2, x3 pairwise distinct. Determine the equation of the altitude D, coming from M3 ; deduce the coordinates of H, point of intersection of...
6. ### Hard polynomial equation

Hi everybody :) Here is the problem : Find all the values of the integer x so that : {x }^{4 }+{x }^{3 }+{x }^{2 }+x +1 =n Where n is a perfect square. I really have no idea of where to begin...

Hi everyone ! I am in a struggle today, with a hard quadratic equation problem : Let's suppose that, with x being an element of [-1;1], we have : |ax^2 +bx+c| <= 1 with a=/=0. ( <= means inferior or equal to) Show that |b| <= 8 and that this...
8. ### Very hard ans unusual quadratic equations. Need help.

Hello everybody, I have 2 problems I cannot solve : 1) (3m-2)x^2 +2mx+3m=0 Can we determine values of m for which this equation has 2 real roots x' and x" such as 0<x'<1<x" ? 2) x^2 -2(2m-5)x+29-20m=0 (1) a) x' and x" being the roots of the equation, calculate, as a function of m the...
9. ### Hard Limit Question

1) Let f(x)= x^3 + x^2 - 2x a. A graph of this function is provided on the next page. Mark the point P((5/4),(-5/2)) and then draw a line through P that appears to be tangent to the graph of f. Call the point oftangency call the point of tangency (a,f(a)) b. Find f'(x). Set up and solve an...
10. ### Not hard equation i got the solution but dont know how to do it

Its about (m-3)x=m(2-x)-2m+1 Find m if x<0 . The solution is m<3/2 just show me the way pls
11. ### 3 really hard integrals

Hi! I would really appreciate any help solving couple of integrals. I probably wasted weeks on them... and small forest worth of paper... 1st should be solved with u-substitution; \int \frac{2^x\cdot 3^x}{9^x+4^x}dx \int \frac{x^3-6}{x^4+6x+8}dx \int...
12. ### Hard Word Problem

A man invited 100 persons in a party, they included Engineers, Scientists and Workers. He had 100 plates for the dinner. Now Engineers saw it and thought why don't we play our game. They said we will need two plates per person for the dinner. Seeing that Scientists too couldn't help, they said...
13. ### Incredibly hard Integral, help wanted

Hello everyone, I'm trying to solve an integral but it really looks hard. I've already tryied it by looking some examples over the internet but I cannot find any. The point here is to attempt to solve the Integral by using all (or almost all) the types of integration: by parts, partial...
14. ### hard pentagon

View image: analitik
15. ### Population with Harvesting ODE so hard

this kind of question has probably always have been the most difficult part of ODE never got used to it HOW IN THE WORLD AM I SUPPOSED TO SOLVE THIS THERE IS JUST NO WAY!!!!!! still they have an answer for it!!!!!!!!!
16. ### Are related rates hard?

I kinda scared of related rates because i heard it's very hard. Any suggestions or advice to help me understand and finish my homework easily?
17. ### Two puzzles our math team gave us

http://puu.sh/gtKpZ/a30cae3959.png <- This is a Location puzzle, meaning the answer is a location. http://puu.sh/gtKr8/a3787c0768.png <- This is a Keyword puzzle, meaning the answer is a word/phrase.
18. ### Hard Problem: (-7/4)e^(5k) + e^(10k) = -2/5

I'm not sure how to solve this equation by hand: (-7/4)e^(5k) + e^(10k) = -2/5 I have no idea where to start with this. What is k? I can factor this to e^(5k) * [ (7/4) + e^(5k) ] = -2/5, but what good would that do?
19. ### Combinatorial-designs- hard proof.

Given a (v, b, r, k, \lambda,) design and a particular block B of it, for 0 \le i \le k let x_i denote the number of other blocks which intersect B in precisely i varieties. Show that \sum^k_{i=0} x_i = b- 1 Please give me a hand.
20. ### Need Help Solving a 2nd Order Nonlinear Differential Equation!

Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1 y''=2ay^3-(a+1)y with a within [0,1] I am pretty much lost on how to go about solving this. It would be greatly appreciated if someone could point me in the right direction on this. Thanks!