# Search results

1. ### Need Help with Trigonometry Problems

For the first problem, can you rewrite the right hand side of the expression, i.e. \cos^2 x in terms of \sin x function? Once you have done that, you then have a quadratic equation in \sin x and you can use the quadratic formula or factoring method to solve for x.
2. ### Challenge Determine the minimum value

Thanks Mark for your so well explained solution to the challenge! Bravo!
3. ### Challenge Determine the minimum value

Determine the minimum value of the function f(x)=x^4-6x^2+8x-3 .
4. ### Challenge Evaluate the sum

Bravo, Mark! (Cool)
5. ### Challenge Evaluate the sum

Given that abx^2=(a-b)^2(x+1). Find 1+\dfrac{4}{x}+\dfrac{4}{x^2}.
6. ### Challenge Quadratic equation that has two roots

Very good Mark!(Cool) And thanks for participating in this challenge problem!(Heart)
7. ### New Buckeye Enters The Fold

Hi and welcome to the forum! If your son has any math problems that he doesn't know how to do, just ask away! we are here to help out! (Smile)
8. ### Challenge Quadratic equation that has two roots

Find all integer valuse of k such that the quadratic expression (x+k)(x+1991)+1 can be factored as a product of (x+p)(x+q), where p and q are integers.
9. ### Challenge Simplify a sum

Beautiful! Thanks for participating, Mark!
10. ### Challenge Simplify a sum

Very good, Mark! The following is the second part of the challenge: Evaluate \prod_{x=0}^{89} (\tan x \cos 1 ^\circ + \sin 1^\circ)
11. ### Challenge Simplify a sum

Simplify \tan x \cos 1 ^\circ + \sin 1^\circ.
12. ### Challenge Find the sum of squares

Aren't you my smartest Mark? Hehehe...:)(Cool) Your solution is of course correct and thanks again for participating my challenge math problem!
13. ### Challenge Find the sum of squares

If x^3=12x+7y and y^3=7x+12y, evaluate x^2+y^2.
14. ### Challenge Solve for x

Very well done, Mark!! And thanks for your constant support to my challenges.(Heart)
15. ### Challenge Solve for x

Solve the equation x^{\log x}=\dfrac{x^3}{100}.
16. ### Challenge Find the sum to infinity of a sequence

Indeed we are...great mind thinks alike? :)
17. ### Challenge Find the sum to infinity of a sequence

Very well done, sweetie Mark!!(In Love) My solution: \dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\cdots=\dfrac{\pi^2}{6} \dfrac{1}{1^2}+\dfrac{1}{3^2}+\dfrac{1}{5^2}+\cdots+\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+\cdots=\dfrac{\pi^2}{6}...
18. ### Challenge Find the sum to infinity of a sequence

If \dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\cdots=\dfrac{\pi^2}{6}, evaluate the exact value of \dfrac{1}{1^2}+\dfrac{1}{3^2}+\dfrac{1}{5^2}+\cdots
19. ### Practice Find derivative of the sum of two quotients

Very well done, Mark! This problem is hard to differentiate if one opts to start differentiating and then simplified later...but if we simplify it first, then what we need to differentiate is only the sine function. Thanks for participating, Mark!
20. ### Practice Find derivative of the sum of two quotients

Find the derivative of \dfrac{\sin^2 x}{1+\cot x}+\dfrac{\cos^2 x}{1+\tan x}.