1
vote
3answers
85 views

How exactly does the response “infintely many” answer the question of “how many”?

I admit that the level of this question is roughly about middle school, but this is what the question asks: The ratio of nickels to dimes to quarters is 3:8:1. If all the coins were dimes, the ...
1
vote
1answer
56 views

Routes to a house

In this city, all the streets that run North and South have lettered names (A,B,C, etc.) and all the streets that run East-West have numbered names (1st, 2nd, 3rd, etc.). As you drive East, the ...
2
votes
4answers
68 views

Contest problem involving primes and factorization

Prove that for any nonnegative integer $n$, the number $$5^{5^{n+1}}+ 5^{5^{n}}+1$$ is not prime. I want only some hints and the method to follow, but I don't need the full solution. Thanks.
1
vote
3answers
26 views

Basic Algebraic Manipulation

How would I solve for $X$ in this instance? I can't figure out how to get the $X$ variables by themselves and the known values on the other side by themselves. $2(4-X)(4-X)+X = 3$
1
vote
2answers
48 views

Amount of Miles

Gary has two cars: His fairly new van and his old clunker station wagon. the wagon currently has 16 times as many miles on it as the van had when the wagon had 3 times as many miles as the van has ...
1
vote
1answer
71 views

How deep would the water be?

The lake created by Hoover Dam on the Arizona-Nevada border has a capacity of 31,250,000 acre-feet. If the whole lake suddenly flooded the Mojave Desert (area 15,000 sq. miles) how deep would the ...
0
votes
2answers
38 views

Finding the distance between the point $(3,7)$ and $x = 0$

In the paper of maths, there was an M.C.Q.S.: The distance of the point $(3,7)$ from $x = 0$ is $3$ $7$ $10$ $8$ So can anyone tell me what was the correct answer and how to ...
6
votes
2answers
562 views

Express y in terms of x

Question: $$ \text{It is given that } y= \frac{3a+2}{2a-4} \text{and }x= \frac{a+3}{a+8} \\ $$ $$ \text{Express } y \text{ in terms of } x. $$ From using $x$ to solve for $a$, I discovered that ...
0
votes
2answers
59 views

How to solve age word problems?

Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age? Is ...
-2
votes
3answers
52 views

How to know number of eggs in this problem?

A women took a certain number of eggs to the market and sold some of them. The next day through her poultry industry, the number left over had been doubled, and she sold the same number as the ...
0
votes
2answers
21 views

Define variable value - General Math

I met a little problem in one of my Math - tasks. Its quite simple: I get to cases = case 1: $(476\cdot x)+220$ case 2: $(278\cdot x)+675$ The variable x have to be a value, so case 1 and case 2 ...
0
votes
1answer
26 views

Proof of transformations to find an approximate value

I have no idea what this questions is asking, or how to go about solving.. can someone please help? Answer:
0
votes
1answer
69 views

Velocity and distance problem

From city A, car a sets on it's road towards city B. 9 Hours later, car b, sets from city B towards city A. The two cars met along the way. At the point of the meeting, car a, passed 240 km more than ...
0
votes
4answers
56 views

How can I solve these equations? [closed]

I can't figure it out, please help :S $$\begin{array}{rcl} 2x + 2xz &=& 0\\ -2y + 2yz &=& 0\\ x^2 + y^2 &=& 4 \end{array}$$ Thanks in advance!
0
votes
1answer
66 views

Distance Question

Two trains set out of two cities, A and B, simultaneously; One from A and one from B. Until the meeting one train has passed $108$ km more than the other. Later, one of the trains arrived at it's ...
0
votes
4answers
45 views

Solve for $x$ when a maximum over $x$ and a constant is involved

This may be a simple question, but I'm not sure how to find the algebraic solution for a problem like: $ax=b+\max(cx,d)$ where $a,b,c$, and $d$ are known. Wolfram-Alpha is not able to give me a ...
1
vote
2answers
85 views

Solving quadratic system

If $a,b,c\in \mathbb{R}$ satisfy the system $a^2+ab+b^2=9$; $b^2+bc+c^2=16$;. $c^2+ac+a^2=25$. Find $ab+ac+bc$
4
votes
2answers
163 views

How to solve for $x$ in $\sqrt[4]{x+27}+\sqrt[4]{55-x}=4$?

I'm trying to guess a method for getting the values that work on this irrational equation: $$\sqrt[4]{x+27}+\sqrt[4]{55-x}=4, x\in\mathbb C$$ After using the formula ...
0
votes
1answer
42 views

Power calculation problem

Three machines perform together a certain job. If only machine A works, to perform the job alone, it would require a hours more than the time required to perform the job by the 3 machines, when they ...
4
votes
3answers
289 views

$\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-…}}}} $, what is the nearest value of $y^2 - y$?

I found this question somewhere and have been unable to solve it. It is a modification of a very common algebra question. $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $, what is the ...
1
vote
1answer
77 views

Show that there is a number between 1 and 1000 such that there is a perfect square

Show that there exists an integer $n \in S = \{1,2, \ldots, 1000\}$ such that $$\prod_{i\in S-\{n\}}i!$$ is a perfect square. I was thinking in trying to prove it by contradiction using the ...
7
votes
3answers
171 views

If $x_1, \ldots, x_6$ are positive real numbers that add up to $2$. Show that:

If $x_1,x_2,x_3,x_4,x_5$ and $x_6$ are positive real numbers that add up to $2$, then: $$2^{12} \leq \left(1+\dfrac{1}{x_1}\right) ...
2
votes
1answer
52 views

Prove that $a=2,b=2,c=2$ for a system of three equations.

Let us consider a system equations : \begin{gather} a^3+b=3a+4\tag{i}\\ 2b^3+c=6b+6 \tag{ii}\\ 3c^3+a=9c+8\tag{iii} \end{gather} I have tried with the following steps : ...
0
votes
1answer
43 views

Norm, limit, and max norm

For any $\vec{u} \in \mathbb{R}^2$ prove that $$\lim_{p\to \infty} \|\vec{u}\|_p = \max (|u_1|, |u_2|)$$ Then, when $p\to\infty$ we get $||\vec{u}||_{\infty}$. And we get the max norm, ...
0
votes
1answer
116 views

Prove using Jensen's Inequality

Let $\alpha_1, \alpha_2, . . . , \alpha_n$ be the interior angles of a convex (but not necessarily regular) n-gon. Prove, that for all integers $n\geq3$: $$\cos \alpha_1 + \cos \alpha_2 + \cdots + ...
0
votes
2answers
69 views

Prove completing the square

Prove that: $x + y + xy - x^2 - y^2 \leq 1$ If I use $-x^2 + xy - y^2$ to start completing the square, I get: $x + y -((x+y)(x-y)) - xy$ I am confused on how to keep going.
0
votes
2answers
107 views

Solving a system of equation

Solve the following system of equations: $\left\{ \begin{align} & 2{{x}^{2}}-5xy-5{{y}^{2}}+x+10y-35=0 \\ & {{x}^{3}}+5x{{y}^{2}}+42=0 \\ \end{align} \right.$ By using a computer, I have ...
1
vote
0answers
68 views

Recommendation for a good book on equation solving theory from the basics

I'm relearning calculus but I often find myself applying algebraic operations to equations mechanically without having a solid understanding of the side-effects of those operations. Such as extra or ...
0
votes
1answer
72 views

Finding speed from little information?

The problem I've been given to solve is read as follows. Two-thirds of the way across a narrow railroad bridge, Willy Gope hears a train coming towards him. He knows that the train's speed is 45 ...
3
votes
3answers
109 views

Finding roots of $-3x^{1.25}-3x+10$

I'm in a math workshop, where one of the problems given was $y=–3x^{1.25} –3x+10$. Much to my frustration, the only stated way to find roots was finding x by trial and error. Is there any way to ...
3
votes
1answer
423 views

Time between 3 and 4 that the hour and minute hands overlap each other?

This problem is on the practice problems for my math club, but I'm not sure how to solve it. What's the exact time that the hour and minute hands overlap each other between 3 and 4 o clock on an ...
1
vote
1answer
110 views

find the value of 1/(2+1/(4+1/(4+1/(…))))

the question is to find the value of this ugly non-stopping fraction $$\frac{1}{2+\frac{1}{4+\frac{1}{4+\frac{1}{\ldots}}}}$$. I have totally no clue; thanks for the help! How am I suppose to solve ...
-4
votes
2answers
128 views

Finding the value of $a^2 + b^2 + c^2 + d^2$

Let $a,b,c,d$ be natural numbers that satisfies $(ab+cd)^2 + (ad-bc)^2 = 2009.$ Find the value of $a^2 + b^2 + c^2 + d^2.$
1
vote
2answers
253 views

$\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$? [closed]

How to prove that $a^2+b^2+c^2=(a+b+c)^2$ given that $\frac1a+\frac1b+\frac1c=0$?
3
votes
1answer
143 views

A simple elementary school math/physics problem - but where's the mistake?

I've come across this problem and managed to get the right answer, but there remains a mystery that I wasn't quite able to solve: the minus sign (or a lack thereof)! Here's the problem and my ...
2
votes
2answers
126 views

How would you interpret this question focusing on problem solving?

The first step of problem solving is to understand what the problem is asking, that is where I am stuck. One of the legs of a right triangle has length 4 cm. Express the length of the altitude ...
1
vote
3answers
97 views

Solving for $(x,y): 2+\frac1{x+\frac1{y+\frac15}}=\frac{478}{221}$

Solving for $x,y\in\mathbb{N}$: $$2+\dfrac1{x+\dfrac1{y+\dfrac15}}=\frac{478}{221}$$ This doesn't make any sense; I made $y+\frac15=\frac{5y+1}5$, and so on, but it turns out to be a very ...
-3
votes
3answers
117 views

Let $f$ be a function satisfying such that $f(xy)=\frac{f(x)}{y}$, what is $f(600)$? [closed]

Let $f$ be a function satisfying such that $f(xy)=\frac{f(x)}{y}$ for all positive real numbers $x$ and $y$. Given that $f(500)=3$, what is $f(600)$?
-2
votes
1answer
50 views

Suppose that $x > y > 0$. Which of the following is equivalent to $\dfrac{x^y y^x}{y^y x^x}$? [closed]

Suppose that $x > y > 0$. Which of the following is equivalent to $\large\dfrac{x^y y^x}{y^y x^x}$? $(x-y)^\dfrac{y}{x}$ $\left(\dfrac{x}{y}\right)^{\large x-y}$ $1$ ...
10
votes
4answers
512 views

The value of $\sqrt{1-\sqrt{1+\sqrt{1-\sqrt{1+\cdots\sqrt{1-\sqrt{1+1}}}}}}$?

How to find value of $\sqrt{1-\sqrt{1+\sqrt{1-\sqrt{1+\cdots\sqrt{1-\sqrt{1+1}}}}}}$ ? I've calculated it by MATLAB for some finite terms and I've got : $0.3001 - 0.4201i$, but I don't know how to ...
0
votes
2answers
48 views

Help with a Function

I'd like some help getting this question on its way, any help would be greatly appreciated. For the following function $$f(x) = \frac1{-(x-5)^2+7}\;,$$ determine: a) The equation of the ...
1
vote
2answers
51 views

Problem Solving using Algebra

If Peter is $7$ years older than Sharon and John is twice as old as Peter, work out how old Peter is if the average of their ages is $19$. Thanks! :)
1
vote
2answers
53 views

How can this be the correct derivative?

I am learning statistics and come across this calculation for Maximum-Likelihood estimator for the Binomial distribution. I don't understand the step from second to third row where they took the ...
0
votes
3answers
80 views

$\log\left(\binom{n}{x} \pi^x (1-\pi)^{n-x}\right)=x\log \pi + (n-x)\log(1-\pi)\;\;?$

$$\log\left(\binom{n}{x} \pi^x (1-\pi)^{n-x}\right)=x \log \pi + (n-x)\log(1-\pi)$$ this is what i have. i dont understand how $\binom{n}{x}$ disappears, but the rest is fine. I tried this, but it ...
5
votes
2answers
238 views

Let $k \geq 3$; prove $2^k$ can be written as $(2m+1)^2+7(2n+1)^2$

Prove: If $k \geq 3$, then $2^k$ can be written as $(2m+1)^2+7(2n+1)^2$, where $k, m, n \in \mathbb{N}$.
3
votes
6answers
333 views

Solving $\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$

Where do I start to solve a equation for x like the one below? $$\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$$ After squaring it, it's too complicated; but there's nothing to factor or to ...
1
vote
2answers
76 views

Solving a system of equation:

Solve for $x,y$: \begin{align} x^3 + y^3&=2\\ x^2 +x + 9y - 3y^2&=8 \\ \end{align} I can find $x=y=1$ by guessing. Please help me solve it without using computer. Thanks Edited, sorry, I ...
2
votes
1answer
62 views

Simplifying $\left|\left|\sqrt{-x^2}-1\right|-2\right|$

How do we simplify the expression $\left|\left|\sqrt{-x^2}-1\right|-2\right|$? This is very confusing. Do they cancel out and become just simply $\sqrt{-x^2}-1-2$?
24
votes
12answers
2k views

Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$

Without the use of a calculator, how can we tell which of these are larger (higher in numerical value)? $$\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$$ Using the calculator I can see that the first one ...
3
votes
2answers
126 views

Using the hypothesis $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ to prove something else

Assuming that $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$$ Is it possible to use this fact to prove something like: ...