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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9 views

Does the term “Proportional” have different meanings?

I have recently been confused by the term "Proportional". This started when I came across 2 different websites that seem to contradict one another when it comes to y = x^2. The first implies that the ...
-4
votes
1answer
23 views

Help me solve for x (it is in the numerator and denominator)

$$\frac {x}{1-x} = e^{\frac {-H + TS} {RT}}$$ Solve for $x$. I cannot figure out what to do. Please help
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2answers
46 views

Function or relation: y^4 = 8x^2

The question under debate: Is $y^4=8x^2$ a function or a relation? We disagree. I say, it's a relation because when I substitute in points I get two outputs for most inputs, and thus it's not a ...
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2answers
30 views

A quick Logarithm question

Did I do this problem right? $\log y= 10 + 2(\log x)$ $y= 10^{10} + x^2$? Edit: How does $10^{\log (x^2)}= x^2$? I can't seem to find an explanation for this. All the websites that I found already ...
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2answers
28 views

Solve using: complete quadratic equation?

$$x^2 - x - 20 > 0$$ $$x^2 - x > 20$$ Step 3: So to complete it, let's use: $1/2$ so it ends up with $x$ as the middle term. $$x^2 - x + 1/2 > 20 + 1/2$$ Step 4: But then: It would ...
-4
votes
1answer
31 views

Solve equation with exponential variables [on hold]

How do I find the set of all $a, b, c$ such that $$ae^t + be^{-t} + c = 0$$ where $a,b,c \in \mathbb R$
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1answer
37 views

How to find an inverse function of $\frac{2x+3}{x-1}$? [on hold]

How to find an inverse function of $\frac{2x+3}{x-1}$ step by step?
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0answers
27 views

Negative Squared Root on Quadratic Equation formula?

I have this basic problem: "In a farm, X animals are integrated. This animals gain weight acoording to this: $500 - 2X$ gr. Which interval of animals can take the farm, if the total weight gain is ...
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2answers
42 views

How to solve the following equation: $\frac{3}{x} - \frac{x-3}{2x+10} + \frac{8}{3x+15} = \frac{4}{3}$? [on hold]

I'm facing difficulties in solving the following equation - would someone mind giving me a hint? $$\frac{3}{x} - \frac{x-3}{2x+10} + \frac{8}{3x+15} = \frac{4}{3}$$ Thanks in advance!
0
votes
1answer
47 views

The real number system [duplicate]

Let $a$, $b$ and $c$ be distinct nonzero real numbers. If $$a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a},$$ then show that $\left|abc\right| = 1$. How do I show the solution to prove it?
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2answers
60 views

Solving $3x^{4}-7x^{3}+2x^{2}=950$ over the rationals

I am asked to find only rational solutions. Factoring by $x^{2}$, I get: $$x^{2}(3x^{2}-7x+2)=950$$ By applying the quadratic formula, I have: $$x^{2}(3x-1)(x-2)=950$$ I don't know how to proceed ...
4
votes
2answers
91 views

Solve the equation $\sqrt{x+5}=5-x^2$

Solve the equation $\sqrt{x+5}=5-x^2$. I have tried to make the substitution $x=\sqrt{5}\tan^2 \theta$ and wanted to make use of the identity $\tan^2\theta+1=\sec^2\theta$ but it didn't work out. I ...
1
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2answers
37 views

$\frac{0}{0}$ means functions have a common factor and can be simplified?

Say for example we have the following function $$\frac{2x+8}{x^2+x-12}$$ at $-4$ both functions have the same value which is zero which means at this point the functions cross. How is it that ...
3
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1answer
28 views

Solving Functional Equations by Limits …

Let f(x) be a continuous function and satisfying the equation : f(2x) - f(x) = x . Given f(0)=1 ; Find f(3)=? My teacher solves this as : f(x) - f(x/2) = x/2 f(x/2) - f(x/4) = x/4 . . . ...
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0answers
16 views

Cost, Total Revenue, Total Profit, Marginal Cost, Marginal Revenue, Marginal Profit, Break Even Point Question [on hold]

the running shoe manufacturer, but use a fixed overhead of $ 270000.00, variable costs of $ 40.00, and a selling price of $ 80.00. (a) Cost C(q)= ? dollars Total revenue R(q)= ? dollars Total ...
4
votes
1answer
17 views

Going from composites to individual functions

$f(g(k(x)))=\sqrt{1+4x^2}$ and $g(k(f(x)))=1+4x$ What is a systematic way to solve for $f$,$g$,and $k$? I never learned anything like this in algebra.
2
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5answers
61 views

How can there be two different answers from two identical equations for the same value of $x$? $(x-1)/(x^2-1)$ and $1/(x+1)$.

Given the following equation: $$f(x) = \frac{x-1}{x^2-1}$$ find the limit of $f(x)$ when $x \to 1$. I know how to solve it, by simplifying the above equation to $f(x)=1/(x+1)$, giving the answer ...
0
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2answers
52 views

Proof if $0\leq a,b<1$ then $a+b<1+ab$

I need to prove that is $0\leq a,b<1$ then $a+b<1+ab$. What I did is see this is equivalent to $a+b-ab<1$. We have: $a+b-ab=a+(1-a)b<a+(1-a)1=1$ as desired. Is there a straightforward ...
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5answers
788 views

Fibonacci number identity.

How do I see that $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$, $n \ge 2$, where $f_1 = 1$, $f_2 = 1$, and $f_{n+2} = f_{n+1} + f_n$ for $n \in \mathbb{N}$?
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1answer
25 views

Understanding Composition Function (fg)(-1) for f(x)=x-3 & g(x)=x^2-8x+15?

Can someone help explain how to do the following composition function to me? (or at least get me started) Find the value of (fg)(-1) if ...
0
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2answers
35 views

I'm having a problem with this number and digits problem. What to do?

During the last election , the total number of votes recorded in the municipality of San Juan was 8600. Had one-third of Estrada’s supporters stayed away from the polls and one-half of Arroyo’s ...
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2answers
77 views

How do I find the exact value of $\cos^2\left(\frac{5\pi}{12}\right)$?

I'm having trouble finding the exact value of $\cos^2\left(\frac{5\pi}{12}\right)$ in radians. I was able to figure out that: $$ \begin{align} \cos\left(\frac{7\pi}{12}\right) &= ...
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0answers
15 views

What's the answer to this number and digit problem? (I'm confused at “exceeds three times the tens digit by 3”)

The units digit of a two digit number exceed three times the tens digit by 3. If the tens digit is subtracted from the units digit, the difference is 7. Find the number.
0
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2answers
45 views

Help with this mathematical induction please? [on hold]

Use mathematical induction to prove that the following is true for every positive integer $n$: $$\dfrac{1}{4}+\left ...
0
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0answers
8 views

Finding the Requested Value of Composition Functions?

I seem to still be having difficulty with understanding Composition Functions in Calculus and wondered if someone might be able to help explain in a way that will make the light bulb "turn on"? For ...
1
vote
4answers
114 views

Why is $\sqrt{x^2} = |x|$? [duplicate]

Why is $\sqrt{x^2 } = |x|$ ? Squaring always produces a positive result, and you obviously square the equation before taking the root of it. So where exactly is the problem?
1
vote
1answer
39 views

Is there a rigorous approach to solving this, instead of trial and error?

This is a question from a 4th grade math book. The solution in the teacher's guide suggests that one might not be able to model the question easily and the best approach may be to solve by trial and ...
0
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0answers
21 views

How to evaluate this simple formula. [on hold]

$\big( \frac 8 {27} \big) ^{\frac 3 2}$ I tried all the ways but couldn't solve this. Any help would be appreciated.
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0answers
22 views

Beginner: Hyperbola asymptotes

Disclaimer: I'm a beginner to asymptotes with hyperbola. Jane Sterling, the author of Algebra II for dummies, writes the following: Whereas Khan (video) solves for y as x approaches infinity (x's ...
0
votes
1answer
15 views

finite-state machine for a system

Every cycle we get a bit $x_t$. We output $1$ iff $$(x_1\ldots x_t) \bmod 5 = 2 \lor (x_1\ldots x_t) \bmod 5 = 4$$ I need to design an FSM (preferably Mealy machine but that doesn't really matter. ...
0
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1answer
68 views

How many times this formula will be used?

Given two equations: if $(b \ge x)$ do this assignment: $b = b-x$ else do this assignment: $b = w - (x - b)$ I know that $w > b$, $w > x$ and $x > 0$. The question is: Given the values ...
2
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2answers
48 views

Firing Solution on a Moving Target

I need to calculate the 3-component $\vec V$, which is the gun barrel vector needed to hit a target moving at a constant velocity. To find this information I'll also need to find $t$ which is the time ...
0
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0answers
22 views

Implementing FizzBuzz game

I need to build an electrical-circuit for the FizzBuzz game. There's a signal, called next which increment the current number by one. The rules are simple - You ...
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0answers
19 views

Simple Equation In One Variable [on hold]

Found both answers by myself, was trying to do it even after posting this. Thank people.
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1answer
34 views

how to solve $2^{2x}-12(2^x)+36=0$ [on hold]

Today I had an exam with the question: solve for $x$: $2^{2x}-12(2^x)+36=0$ I just can't figure out how to solve it, can someone please show me.
0
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2answers
37 views

How do I solve inequality $\frac{2x-3}{x+1}\leq 1$?

How do I solve inequality $\frac{2x-3}{x+1}\leq 1$? Here is my thought process: $2x-3 \leq x+1$ so $x \leq 4$ So in interval notation, this is $(-\infty$,4]$ but apparently this is not ...
0
votes
5answers
81 views

Is it okay to use the quadratic equation in an inequality?

I've been trying to solve this problem: A chicken cost $38$ units. The weekly cost of preparing $x$ chickens is given by the equation: $P = -0.1x^2 + 1190 + 28x$. How many chickens must be sold ...
2
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0answers
21 views

Coming up with a function or a single graph, given its characteristics (pre-calculus)

Give an example of a function or a single graph which has the following characteristics: Hole at $(3,-1)$ Domain is all real numbers except $3$ Local minimum at $(-1,-2)$ Local ...
2
votes
1answer
40 views

Is my answer wrong?

As their father told them, the elder son took half of the money that was in the box and 200 Dhs. After that, the junior son came and did the same thing. Finally, the little son came, did the same ...
1
vote
5answers
52 views

How do I solve $x^4-3x^2+2=0$?

How do I solve $x^4-3x^2+2=0$ ? I would appreciate some kind of hint here. I have no clue how to start this problem.
1
vote
1answer
31 views

Identifying the formula for a quartic graphic

I am attempting to help someone with their homework and these concepts are a bit above me. I apologize for the terrible graph drawing. I am using a surface pro 3 and it has an awful camera so I can't ...
-2
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2answers
37 views

Please help me with this sigma notation [on hold]

Use the properties of summation to evaluate the following: $$\displaystyle \sum^{4}_{i=1}(i^2-3i)$$
0
votes
3answers
32 views

Why is the limit of this graph not 4.3?

I just took an online exam as part of a Precalculus course, and one of the problems on my test was as follows: Estimate $\lim \limits_{x \to 2} f(x)$ from the graph below. The available ...
5
votes
3answers
56 views

How do you factor $\frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}=$?

\begin{align} & \frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}= \frac{2x^2-x-1}{(x-3)(x+3)} \cdot \frac{x+3}{2x+1} \\[10pt] = {} & \frac{2x^2-x-1}{(x-3)} \cdot \frac{1}{2x+1}= ...
-5
votes
3answers
32 views

one number is six more than another.The sum of the two numbers is 28. What are the numbers? [on hold]

one number is two more than another.The sum of the two numbers is 20. What are the numbers?
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votes
2answers
33 views

Need help to understand a math task about algebraic and parametric equations

Can anybody please explain this for me?: Find the algebraic and parametric equations of the circle with centre (-2,3) that passes through (1,-1) How do I find the algebraic and parametric ...
14
votes
4answers
3k views

How to find out which number is larger without a calculator?

So I have a question which is: Which is larger? $$2.2^{3.3} \text{ or } 3.3^{2.2} $$ Now I need to find out with using a calculator but the answer is $3.3^{2.2}$. The only thing I could think of ...
-4
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1answer
23 views

Word problem including time [on hold]

Two vans are 420 miles apart when they begin traveling toward each other. One can goes 50 mph while the other goes 55 mph. How long do they drive before they meet?
-1
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3answers
27 views

Guaranteed Profit on a Roulette wheel: Does $N$ exist?

I'm looking for a good answer that can be explained to someone without much maths. If a casino spins a roulette wheel enough times, the probability the casino makes a profit $\to$ 1 as $N \to \infty$ ...
5
votes
4answers
117 views

How many ways to write $2010$?

Let $ N$ be the number of ways to write $ 2010$ in the form $ 2010 = a_3 \cdot 10^3 + a_2 \cdot 10^2 + a_1 \cdot 10 + a_0$, where the $ a_i$'s are integers, and $ 0 \le a_i \le 99$. An example of ...