Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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0
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4answers
58 views

How to find x intercept?

$y=(x-4)^3+1$ So, to find the X intercept. $0=(x-4)^3+1$ How to solve the equation $0=(x-4)^3+1$ ? Please explain with steps.
1
vote
0answers
79 views

Find the GCD of the minimum non-negative values of $a$, $b$ and $c$, given that the equation $x^4+ax^3+bx^2+cx+1=0$ has real roots only.

What is the GCD of the minimum non-negative values of $a$, $b$ and $c$, given that the equation $x^{4}+ax^{3}+bx^{2}+cx+1=0$ has real roots only?
3
votes
4answers
140 views

If $p$ is a prime and both roots of $x^{2} +px−444p=0$ are integers what is $p$

If p is a prime and both roots of $x^{2}+px−444p=0$ are integers, what is $p$ I got that for the roots to be integers the discriminant must be a perfect square. Thus, $p(p + 1776)$ must be a ...
2
votes
1answer
72 views

How do I algebraically manipulate this?

From a paper that I have been reading, I have: $n \pi = +\sqrt{(+k_2+\sqrt{k_2^2-4k_3k_1}) \times \dfrac{1}{2k_1}}$; where $k_1 = (1-\dfrac{\alpha^2 \lambda^2}{\zeta^2})$; $k_2= \lambda^2[\Omega + ...
0
votes
1answer
38 views

What's mean 'the value $1$ is unchanged under this mapping,find the other value of $x$ which is unchanged'

$$f(x) = \dfrac{4 + x}{2 + 3x}$$ Given that the value $1$ is unchanged under this mapping,find the other value of $x$ which is unchanged.
0
votes
2answers
25 views

efficient clean up

There is a chemical spill. 3 crews are called in and asked to estimate how long it would take them to clean the spill if they worked on their own. The respective estimates were 46, 51, and 55 days. If ...
0
votes
3answers
65 views

For $x+y+z=0$, if $x$ and $y$ are divisible by some integer $k$, then so is $z$.

If k|x and k|y and x+y+z = 0, then k|z. Here, "k|x" means that $k$ is a divisor of $x$ and $x,y,z,k \in \mathbb{Z}$ What strategy would you employ to prove this?
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votes
5answers
87 views

Factorization of a degree three polynomial

So I was doing some Vector Calculus homework and was working with Lagrange Multipliers, but then I came across a polynomial that I either forgot how to factor or never learned. I plugged it into ...
0
votes
2answers
62 views

How to prove this statement and its negation?

Assuming that you're dealing with real numbers, d ^ 2 = e ^ 2, then d = e Why would it be true? << corrected, it is not true! thanks to posters What is the negation and is it true?
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4answers
200 views

Adding fractions is not at all obvious

Why does $\frac{5}{4} + \frac{2}{3}$ need to be rewritten as $\frac{15}{12} + \frac{8}{12}$ to be added? It's not obvious. I'm looking towards the fact that any integer can be rewritten as $x=qy$ ...
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3answers
171 views

Domain/range of composition function

$$f: \mathbb{R} \to \mathbb{R}, f(x) = sin x. \\g: \mathbb{R} \to \mathbb{R}, g(x) = e^x.$$ Need domain/range of compositions. That's what I got, but I'm not 100%: $$f \circ g = sin(e^x)$$ Domain ...
1
vote
3answers
120 views

How can this trig equation be simplified?

We have $9+40\sin^2x=-42\sin x\cos x$. I know this simplifies to $7\sin x+3\cos x=0$, but how?
1
vote
2answers
65 views

Ratio and proportion problem

Question: If $$(a+b):(b+c):(c+a)=6:7:8$$ and $a+b+c=14$, then find the value of $c$. My solution: $$\frac{(a+b)(c+a)}{(b+c)}=\frac{(6)(8)}{7}$$$$\Rightarrow \frac{ac + a^2 + bc + ba}{b+c} ...
0
votes
2answers
304 views

Why does $\sin^{-1}(\sin(\pi))$ not equal $\pi$

And when does $\sin^{-1}(\sin(x)) = x$
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2answers
37 views

Maximum value of an expression,Exponential form terms,

$$S=(150-3x)^{20}(2x-50)^{30}$$ What is the max value of S? Given that 25< x < 50 Answer is $3^{50} \cdot 10^{50}$. I need the explanation.
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2answers
203 views

What's the maximum deviation from loan amortization

Suppose you have a loan with principle P and fixed interest rate i compounded daily. Suppose you make fixed payments every month, but not on the same day. The only constraint is that you make every ...
5
votes
5answers
462 views

Is this trig step correct?

$\sin^{-1}(-\sin(x))$ = $-\sin^{-1}(\sin(x))$ Can the minus be taken out like this?
4
votes
4answers
185 views

If $a+b+c = 7\;\;,a^2+b^2+c^2 = 23$, then $a^3+b^3+c^3=$

If $a,b,c\in \mathbb{R}$ and $a+b+c = 7\;\;,a^2+b^2+c^2 = 23$ and $\displaystyle \frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1} = 31$. Then $a^3+b^3+c^3 = $ $\bf{My\; Trial\; Solution::}$ Given ...
1
vote
2answers
46 views

Proof using binomial coeff

I don't understand the step between left side and right side of my ? I
3
votes
4answers
117 views

Values of square roots

Good-morning Math Exchange (and good evening to some!) I have a very basic question that is confusing me. At school I was told that $\sqrt {a^2} = \pm a$ However, does this mean that $\sqrt {a^2} ...
0
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3answers
1k views

$4^x-4^{x-1}=24$ what is the value of $(2x)^x$?"

So, every week our teacher gives us a very difficult question worth 1 point and I can never get them right, so I would highly appreciate the person who tells and explains, in good detail, why this ...
3
votes
3answers
71 views

Writing $x^2+y^2+z^2$ as a polynomial combination of $xyz$, $x+y+z$, and $\dfrac1x+\dfrac1y+\dfrac1z$

Can we write $x^2+y^2+z^2$ as a polynomial combination of $xyz$, $x+y+z$, and $\dfrac1x+\dfrac1y+\dfrac1z$? What about $x^3+y^3+z^3$?
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vote
2answers
221 views

How is the sin function being rewritten?

I'm working through a trigonometry book and was shown this equation being worked out. I don't understand the rules for doing a particular step: $$\begin{align} A &= A\sin(x-vt) \\ 1 &= ...
0
votes
1answer
473 views

What's the general way to solve worker/time/job problems?

The problem says "In a factory, m workers work h hours to do j jobs. If p new workers are hired, how many hours will the work force have to work to do j jobs?" I worked out the answer logically, but ...
5
votes
4answers
301 views

How to solve $x^3 - 2x^2 -16x+16=0$?

How to solve $x^3 - 2x^2 -16x+16=0$ ? I tried to factor out $x^2$ but it doesn't work..any hints? Ok I tried to use rational root theorem and have possible answer $\pm 1, \pm 2, \pm 4, \pm 8 , \pm ...
1
vote
1answer
280 views

Restrictions on function domain — word problem

Suppose you're to build a $200~\text{m}^3$ fuel tank that has a cylindrical middle part with hemispheres at each end. Suppose you're given the restriction that the maximum allowable length of the tank ...
1
vote
0answers
22 views

Calculating duration of a section with knowledge of mid-point of consecutive sections

Having a brain freeze on this, I have a nagging suspicion this is very straightforward but can't see it and attempts thus far have produced nothing. There are say, n items of duration x1, x2, x3 etc. ...
2
votes
2answers
127 views

Find value of $r$ and the limit

For some $r \in \mathbb Q$, the limit $$\lim_{x \rightarrow \infty}x^r.\frac{1}2.\frac{3}4.\frac{5}6......\frac{2x-1}{2x}$$ exists and is non zero What is that value of $r$ and what is that limit ...
-1
votes
5answers
130 views

What is $x^{1/2} + x^{-1/2}$

Would these two terms cancel out and be zero or can they not be put together since technically the exponent is different? EDIT: I am working on $x^{1/2} + x^{-1/2}$ not $x^{1/2} = x^{-1/2}$
14
votes
3answers
189 views

Finding the real solutions to $16^{x^{2} + y } + 16^{y^{2}+ x} = 1$

We have , $16^{x^{2} + y } + 16^{y^{2}+ x} = 1$ , then we have to find all the real values of $x$ and $y$.I tried this question but i am not able to proceed because I am not able to simplify this ...
0
votes
4answers
305 views

Find the three consecutive numbers

I have my problem here. I can't solve it on my own. I need a solution to prove my answer. Does anybody know this? thanks "Find the three consecutive numbers that have the property that the square of ...
0
votes
1answer
53 views

Functional equation on quaternions

Let $\Bbb H$ be the quaternions and $m:\Bbb H\to \Bbb R$ satisfy the multiplicative functional equation $$ m(pq)=m(p)m(q) $$ for all $p, q\in \Bbb H$. How to represent $m$ in terms of multiplicative ...
2
votes
2answers
71 views

How to get Bill's age

I have a word problem here and I still don't know how to solve this. Please help me. Thank you. "Bill, my second oldest, is twice as old as one of my three other children. Joan is three times as old ...
0
votes
1answer
52 views

How to solve logarithmic function

I am still confused with my solution about Logarithmic function. Does anyone know how to solve this? Do you have links about logarithm in connection to this problem? thank you 4log 2 x - 2log 2 y = ...
0
votes
2answers
122 views

what is i in factoring equations and how do i understand and apply it?

I am currently in Advanced Algebra-ii and we are working with polynomials however I did not understand the lesson where we learned about the number i or how to apply it when factoring or, in general, ...
0
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4answers
456 views

Grade 10 algebra question

Simplify the following: $\left ( 8^{4+2a} \right )\left ( 16^{a-1} \right )\div 4^{3a+2}$ I don't know how to simplify this expression.
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2answers
92 views

Non-linear systems help!

I have a non-linear system of equations, $$\left\{ \begin{array}{rcl} x^2 - xy + 8 = 0 \\ x^2 - 8x + y = 0 \\ \end{array} \right.$$ I have tried equating the expressions (because both equal 0), which ...
1
vote
2answers
60 views

Simple word problem - create equation

I need help forming the equations, I don't want the answer, I just want assistance in finding the answer. Variables have already been declared as the following C = Cost b = number of loaves baked ...
8
votes
7answers
859 views

Prove no real number satisfies $x^{2} = -1$

I ran a search, but, oddly enough, I can't to find a similar question on here. (If so, kindly point me in that direction, and I'll take this one down.) It seems like a pretty basic question in real ...
1
vote
1answer
42 views

Draw following set in $\Bbb{R}^3$

How can I draw following set in $\Bbb{R}^3$? $$ M = \left\{(x,y,z) : \sqrt{x^2 + y^2} \le z \le 1 \right\} $$ I have the answer in the book but I don't want to check it before i try to solve it ...
0
votes
2answers
42 views

Express $\lg \frac{y}{x^2}$ in terms of $a$ and $b$.

If $\lg x^2y = a$ and $\lg \frac{x}{y}=b$,Express $\lg \frac{y}{x^2}$ in terms of $a$ and $b$. I did this, I don't know whether it right or wrong! $\lg x^2y=a$ can be written as: $lgx^2\cdot\lg y=a$ ...
3
votes
3answers
65 views

Correct standard form for the equation of a line?

So I was tutoring an Algebra 1 student yesterday and we were reviewing the three forms in which one can write the equation for a line: point-slope form, slope-intercept form and standard form. I told ...
2
votes
1answer
43 views

An inequality question

The question says that $x > 0$ and then we have to prove that $(x + 1)^{1/2} < 1 + (1/2)x$. I tried this question and proved that $(x + 1) < (1 + (1/2)x)^2$ but after this I am not able to ...
0
votes
1answer
208 views

Show that lines created by certain points on the parabola intersect at the directrix?

Edit: I got the answer by finding points of intersection between the line passing through B and the focus and the parabola, but it didn't seem like the best solution. Any other ideas? The Segments ...
0
votes
1answer
149 views

learn math, again

I am an international student. I am going to apply for a MA program in economics but before doing that, I want to refresh all my math knowledge. I have to take the GRE so I need to re-learn ...
10
votes
6answers
8k views

How can you find the cubed roots of $i$?

I am trying to figure out what the three possibilities of $z$ are such that $$ z^3=i $$ but I am stuck on how to proceed. I tried algebraically but ran into rather tedious polynomials. Could you ...
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votes
2answers
45 views

What Percent of two numbers to get to one [closed]

How can I calculate the missing number using the percent and the the sum? More specifically, $7$% of what number will equal $100000$?
4
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0answers
65 views

Is there a name for systems of equations with min and max functions included?

In a big project I'm working on, I'm running into systems of equations that look like the following: $$a = \min(b, c)$$ $$b = d^2 + a$$ $$c = \max(a + b, d)$$ Basically, nonlinear systems of ...
4
votes
2answers
80 views

Solving for $x$ in $a^x / x = b$

I've ended up with an equation of the form $a^x / x = b$ and I'm trying to solve for $x$ but I can't isolate it. I always end up with one of the $x$'s as the exponent of $e$ or in a log function.
4
votes
2answers
119 views

Prove that $3^{n+1}+3^n+3^{n-1}$ is divisible by $13$.

Prove that $3^{n+1}+3^n+3^{n-1}$ is divisible by $13$ for all positive integral values of $n$. I tried: $3^n \cdot 3^1+3^n+3^n\cdot\frac{1}{3}$ Then what should I do next? Help please?