# problems

1. ### Couple of elementary geometry problems

1. In triangle ABC AB=BC=4, angle ABC=30 degrees. On the outside of sides AB and BC, equilateral triangles ABD and BCF are constructed. Lines AF and CD intersect in point O. Find angles of the triangle AOC and distance between lines AC and DF. 2. Bisectors of angles A and B of parallelogram...
2. ### I need problems

I need problems - like factoring or simplifying polynomials, solving polynomial equations, or problems that are solved using polynomials; - progressions and series, and induction related to these; - logarithms and logarithmic equations; - Trigonometry: proving trigonometric expressions and...
3. ### Trigonometry problems

(1) If z_1 \neq z_2 and z_1 , z_2 \in (0,\pi ). Prove that \: \sin\left(\frac{z_1 +z_2 }{2}\right) > \frac{\sin(z_1 ) +\sin(z_2 )}{2}. (2) Find all pairs (x,y) such that x^2 +2x\cdot \cos(xy)+1=0. (3) Find the number of solutions of the equation \sin(x)=\frac{x}{n} \; , where n\in \mathbb{N}...
4. ### Help turning word problems into equations please...

Hello, my class has just started exploring rational equations. I have no problem solving the equations on their own but when I need to convert information into these equations I can confuse myself. If anyone can help me with turning these two problems into rational equations, I'd be really...
5. ### How can probability theory solve the most complicated problems of five unknowns?

Greetings to All! How to solve such a difficult task? Perhaps there are complex theorems that only enlightened minds can understand? Value: q; w; u; h; m; Is known Value: A; B; C; D; E; Unknown Value: X; The same q = X * A w = X * B u = X * C h = X * D m = X * E Need to...
6. ### How to do these problems?

1) Given that x = 2a^5 = 3a^2, what is the smallest possible value of x? 2) Suppose 3 distinct numbers are chosen from 1,2,.....,3n with their sum equal to 3n. What is the largest possible product of these numbers?

Does there exists a brach of mathematics, if exists, perhaps in computational mathematics, researches the properties of multiple nesting functions where every nested function is somewhat simple, such as piecewise linear function?

9. ### Highschool website for Algebra/Geometry with real life applications or problems

I tried to search something related to real life situations in algebra and in geometry but the only thing I found was a torrent named Mathematics Describing the Real World(with videos trying to explain some theories but with less examples from the real world) and a free website named Don't...
10. ### How do you do these problems?

1. How do you use the composite properties to show that an equation is an identity?With this equation.cos(Î¸-180) = -cosÎ¸ 2. How do you use the composite argument properties to transform the left side of the equation to a single function of a composite argument...
11. ### Concavity and Second Derivative Test Problems Help

Can you help on these sets of problems? I don't understand entirely how to do them, and I have a test coming soon, so I could really use your help. Thanks. Concavity and the Second Derivative Test 2.$\ \ \$Suppose you are given a formula for a function $f$. a)$\ \ \$How do you determine...
12. ### Derivative problems help

Here are some of my practice problems: csc(y^2)=5x+4 and 2x^2+3=e^(2y)^3 Can you show me the steps on each one individually in detail so I can better understand how to do it?
13. ### "Finding Inflection Points" Math Problems Help #2

"Finding Inflection Points" Math Problems Help 4 Let f(x)=-2x^6+15x^5. For what values of x does the graph of f have a point of inflection? I found the second derivative and when factored leaves me with: -60x^3(x-5). So, I figured the answer is just x=5 but my friend told me its zero as...
14. ### "Finding Inflection Points" Math Problems Help 3

Ok this other inflection problem: Let h(x)=x^5+5x^4. For what values of x does the graph of h have a point of inflection? I am stuck on what to do after the second derivative which I found was: 6x^1+60x^2. I tried to factor it which gave me: 6(10x^2+x), but then I don't now how else to factor...
15. ### "Finding Inflection Points" Math Problems Help

I am just learning this new topic at school, and was hoping that you can help me with this example my teacher provided me. The problem is: Let f(x)=-2x^4-8x^3+180x^2. For what values of x does the graph of f have a point of inflection? I understand that you have to do something with the second...
16. ### Does anyone else work on American Mathematical Monthly problems?

I was wondering who else works on these? I think they are fun.
17. ### Advice on solving calculus optimization & related rates problems?

Hey. I'm looking for your advice on these 2 topics which are hard to master. Surely there's nothing common between every question and the other except the calculus you use, but i need to know what mistakes you used to fall in during solving these problems, advice / notes / experiences you...
18. ### Number sequence problems

I really tried to solve them, and I do not have access to the answers. The sequences always have very simple rules behind the patterns, so I'm guessing that the simpler the pattern you found the more correct it is. The problems and what I could think of: 1) 37, 8, 98, 1, 311, 821, 541, ...
19. ### Math Class Problems

Hi, I'm a freshman who is taking Algebra 2, Geometry and Trig all this year. We are doing Geometry right now. The problem is that I failed the last 3 tests and I am freaking out. I don't want to drop the class but if I continue like this I will be forced to drop it. Please help!! I need help...
20. ### Struggling with 2 integration problems

So while I'm pretty confident about what the final answers are,but the way I solved the question and the steps they want us to do aren't really matching so I was hoping someone could help me out with these steps?