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.

learn more… | top users | synonyms (2)

0
votes
1answer
20 views

Which compound interest formula would you use in this situation?

\$38,900 is used to reduce a debt of \$900,000 immediately. Then \$3,055 is paid every month. The interest rate would than be fixed for the next 4 years at the rate of 4.3% p.a. (Does not say it is ...
7
votes
6answers
532 views

How to solve the inequality $x^2>10$ using square roots?

Solve the inequality: $$x^2>10$$ How am I supposed to do this? It doesn't make sense when I take into account that if $x^2=10$ then $x=+\sqrt{10}$ and $x=-\sqrt{10}$ But how am I supposed to ...
1
vote
1answer
19 views

Proof, that equation decribes trace of curve, which is supposed to be simple

The equation, representing the trace of the curve $$ \varphi(x) = (\cos^3(t), \sin^3(t)) $$ is $1 = x^{\frac{2}{3}} + y^{\frac{2}{3}}$. Proof: Let $(x,y) = (\cos^3 t, \sin^3 t)$, then $x^{1/3} = ...
1
vote
2answers
49 views

Solve for positive reals

Solve for positive reals $x,y$ $(x+y)(1+\frac{1}{xy})+4=2(\sqrt{2x+1}+\sqrt{2y+1})$ I started by accumulating the terms of $x$ and then used AM-GM inequality but unsuccessfully....
2
votes
3answers
110 views

Mathematical way to solve integer numbers $217 = (20x+3)r+x$

Is there any mathematical way to find the integer numbers that solve the following equation: $$217 = (20x+3)r+x$$
0
votes
1answer
41 views

Find polynomials $f (x)$, $g(x)$, and $h(x)$

In an elementary Algebra book (101 problems in Algebra) there was a question I solved but when I looked at the solutions I didn't get it. it says find Polynomials $f(x)$, $g(x)$, $h(x)$ such that for ...
1
vote
1answer
34 views

Domain and Range of relations

I am having problems understanding how to solve/find the domain and range for these 2 equations. 1) $y-3x^2 = 2$ 2) ${(x,y); x=3}$ Any help would be much appreciated, Thanks!
0
votes
1answer
34 views

How can I find the R values

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N= R - S \end{cases}$$ - And I have the $B$ values, e.g : 834343, 3253538, ...
1
vote
3answers
29 views

Calculating the angle for a path between two nodes in a graph

I want to (programatically) draw an edge between two nodes in a graph, starting on the outside of the nodes. Below is an illustration of what I'm (poorly) trying to describe: I have the $(x,y)$ ...
0
votes
1answer
39 views

Is there a name for these binary operations?

In computer programming, I often encounter the need to give the binary operations: The greatest multiple of $y$ that is not greater than $x$ $41 \circ_1 6 = 36$ $3.2 \circ_1 0.5 = 3$ The least ...
0
votes
3answers
31 views

Calculating the selling price of a house, given the mortgage, commission, and closing costs

I'm trying to help my wife study for her real estate exam, I thought I was good at math (although I haven't done any in years). Here is the question at hand : You sell a home for a client, and ...
2
votes
2answers
84 views

Any idea how to linearize this equation? $X^2-Y^2=aZ+bZ^2$

The intention is to linearize this equation $X^2-Y^2=aZ+bZ^2$ into something which looks like $Z=mX+nY+c$ so that a graph of $Z$ against $X$ or $Y$ can be plotted. X,Y,Z are variables while a,b,c are ...
0
votes
0answers
38 views

Easy leg and heads problem

Some chickens and rabbits have a total of 100 feet. If each chicken is exchanged for a rabbit and each rabbit is exchanged for a chicken there would be a total of 86 feet. How many chickens are there? ...
1
vote
2answers
30 views

Sketching graphs abs value functions

how do I go forward with sketching the graphs of the following two functions? i) $y(t)=|2+t^3|$ ii) $f(x)=4x+|4x-1|$ thanks in advance!
0
votes
5answers
65 views

Solving limit given a limit

Given the fact that $$\lim \frac{\sin(h)}{h}=1,\ \mbox{as}\ h\to0$$ compute the following limit: $$\lim\frac{\sin(x+h) - \sin(x)}{h}\ \mbox{as}\ h\to0.$$ How would I go about solving this problem? ...
7
votes
3answers
172 views

Logarithm Equality

$$\sqrt{\log_x\left(\sqrt{3x}\right)} \cdot \log_3 x = -1$$ I am not entirely sure how to go about solving for $x$. I cannot square each side because the product isn't $≥ 0$, I can't think of any ...
0
votes
3answers
52 views

Capitalization of interest

I've got quiet a strange problem but a simple one I guess. So I have a starting sum of 10 and I would like to know how many years need to pass to achieve 30000 with 32% interest applied every 2 years. ...
3
votes
3answers
37 views

$x$-intercept of cosine graph

I am having problems understanding how to find the $x$-intercept of a cosine graph. Example: $10\cos(x/2)$ Answer:$((2n + 1)\pi , 0 )$ I have the answer just need help understanding the steps, ...
2
votes
2answers
35 views

Expansion of Logarithms with Cube Roots

Does the following expand to the following $$ \log_6(11^6\sqrt[3]{12}) $$ = $ 6\log_6(11) + \log_6 (\sqrt[3]{12})$
4
votes
2answers
27 views

Logarithm Expansion Question

How do you expand the following logarithm: $$ \log_5 \left(\frac{u}{v^3}\right)^6 $$ The result I got was: $$ 6\log_5u -18\log_5v $$ Is that fully expanded?
1
vote
3answers
45 views

Vertical asymptote of $h(x)=\frac{x^2e^x}x$

$$h(x)=\frac{x^2e^x}x$$ The function h is defined above. Which of the following are true about the graph of $y=h(x)$? The graph has a vertical asymptote at $x=0$ The graph has a horizontal ...
2
votes
2answers
47 views

Conditions of Continuity (Limits)

On a math test, for my online Honors Pre-Calculus course, that I recently took I got this question wrong and don't understand the explanation: Suppose $f(x) = \begin{cases} x^2-2, & x \not= 2 ...
1
vote
5answers
88 views

Identity with logarithms?

Is it correct? $$(\log\,n)^{(\log\,n)} = n^ {(\log\,\log\,n)} $$ If yes and they are equal, how can I get $(\log n)^{\log n}$ from $n^{\log \log n}$ ? Thanks.
0
votes
1answer
53 views

how can I find equation variables?

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N=S-R \end{cases}$$ - And I have the $B$ values, e.g : 173, 283, 2343, 834343 ...
-7
votes
1answer
34 views

Parameter in a system of equations [closed]

Consider the linear system ${\begin{cases} kx+z=1 \\x-y+z=-3 \\ x+y+kz=2 \end{cases}}$ Determine the values of k such that: The system has a unique solution. The system has infinitely many ...
1
vote
3answers
144 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
3
votes
0answers
81 views

Simplifying $\sqrt[3]{a\pm\sqrt{b}}$

Let $$x=\sqrt{a\pm\sqrt{b}}$$ We know that $$x=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}\pm\sqrt{\frac{a-\sqrt{a^2-b}}{2}}$$ But, what about cubic root? Let $$y=\sqrt[3]{a\pm\sqrt{b}}$$ Is there any formula to ...
4
votes
4answers
493 views

What is the non-trivial, general solution of these equal ratios? [closed]

Provide non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ $a=?, b=?, c=?$ The solution should be general.
1
vote
2answers
37 views

Radical Inequality

$\sqrt{2x-1}$ + $\sqrt{3x-2}$ > $\sqrt{4x-3}$ + $\sqrt{5x-4}$ I have attempted to solve this by squaring each side, resulting in $5x + 2\sqrt{2x-1}\sqrt{3x-2} - 3 > 9x + 2\sqrt{(4x-3)(5x-4)} - 7 ...
2
votes
3answers
314 views

How to solve inequalities with absolute values on both sides?

If you have an inequality that has two absolute value bars like $|4x+1|<|3x|$, how do you go about doing this? I know that if $4x+1<3x$, then those $x$'s will work but what else do I do? I think ...
1
vote
1answer
31 views

How do I proceed from here on finding the Binet's formula via generating functions?

So, I'm stuck with the algebra for the nth number on the Fibonacci sequence in here. I managed to get to the part where $G(x) = \frac{x}{1-x-x^2}$ $=$ $\frac{x}{(1-\alpha x)(1-\beta x)}$, and I know ...
0
votes
1answer
47 views

Distance to the perimeter of a circle with given radius, distance traveled from origin, and direction

I am programmer by trade but am running into some trouble with a geometry problem. I basically want to start at the center of a circle, travel any distance within the radius, turn any direction, and ...
4
votes
5answers
142 views

How to solve this inequality? From MSU entrance exam '66

$\frac{\log _{10}\left(2\right)}{\log _{10}\left(\sin \left(x\right)\right)}\le \frac{\log _{10}\left(4\sin ^2\left(x\right)\right)}{\log _{10}\left(\sin \left(x\right)\right)}$ From the title. Not ...
0
votes
1answer
35 views

What method is used to derive at the function to use in the squeeze theorem?

In every exam in the past $5$ years of Calculus A the question has popped up: Use the squeeze theorem to evaluate the $\lim_{x\to n} f(x)$ where $f(x)$ took many forms from a normal algebraic equation ...
-1
votes
0answers
28 views

Plane bearing problem [closed]

Philadelphia is 420 miles due east of Columbus, Ohio. A plane flying 200 mph leaves Philadelphia at noon and flies west for 1 hour. It then veers off its course and flies South 80 degrees 30 minutes ...
3
votes
4answers
52 views

Simplify the following compound fraction:

$$\frac{2x+1}{\frac{3}{x^2}+\frac{2x+1}{x}}$$ My calculator says the final answer is $$\frac{x^2(2x+1)}{2x^2+x+3}$$ Please show the work. Thanks.
0
votes
4answers
42 views

Simplify the following complex fraction:

$$\frac{9/x^2}{\large\frac{x^2}{25}+\frac{x^2}{15}}$$ I have attempted to solve this problem a multitude of times and each time I get a different answer. Is it $\frac{360}{x^2}$, $\frac{360}{x^4}$, ...
0
votes
3answers
99 views

Solving $2X=X^2$ [closed]

When does this equality hold: $2X = X^2$ ?
0
votes
2answers
29 views

$x_1,x_2,x_3,x_4$ are in Harmonic Progression $\Rightarrow (x_1-x_3)(x_2-x_4)=4(x_1-x_2)(x_3-x_4)$

$x_1,x_2,x_3,x_4$ are in Harmonic Progression I need to show $$(x_1-x_3)(x_2-x_4)=4(x_1-x_2)(x_3-x_4)$$ I tried assuming reciprocals are in Arithmetic Progression, but after huge calculation I did ...
-1
votes
0answers
21 views

Equation Inverse vs Solution Domain [closed]

Is finding the solution in a domain of a equation the same as doing the inverse operation? Example: Domain of $x$: $[1,2,3]$ $5x - 1 = 9$ ? I would do the inverse operation, but my teacher tells ...
3
votes
1answer
40 views

Find zero of sum of 4 modified Bessel functions

I am trying to find the (positive) root of the function $f(x) = I_{-3/4}(x) + I_{3/4}(x) - I_{-1/4}(x) - I_{1/4}(x)$ where $I_\alpha(x)$ denotes the modified Bessel function of the first kind. ...
5
votes
2answers
66 views

Ordered pairs of Integers $(x,y)$ which satisfy $x!\cdot y! = x!+y!+2$

Total no. of ordered pairs of Integers $(x,y)$ which satisfy $x!\cdot y! = x!+y!+2$ $\bf{My\; Try::}$We can write the given equation as $x!\cdot y!-x!-y!+1 = 3\Rightarrow \left(x!-1\right)\cdot ...
1
vote
1answer
34 views

Pre- calculus and calculus practice questions

I'll be taking pre-calculus this fall, and I am wondering if anyone on here can recommend a good problem solving workbook with lots of questions for practice.Also,any ideas for calculus I and calculus ...
0
votes
1answer
14 views

Is it necessary to check contrains when solving absolute vlaue inequalities?

For example, let's say we have an absolute quadratic function $f(x)$ which is equal to $|g(x)|$, a quadratic function When faced with solving the following inequality: $f(x) < a$ we have $-g(x)$ ...
0
votes
1answer
33 views

How to find limits involving trigonometric functions as $x\to 0$?

Problem: find the limit as $x\rightarrow 0$ of $\dfrac{\tan(3x)}{\sin(2x)}$ $\dfrac{(\sin(2x) + 3)}{(\cos(7x)-8)}$ Note I am able to solve the first one using l'Hopitals, but I really want to be ...
0
votes
4answers
50 views

Find domain and range of $(f \circ g)$ for $f(x)=\ln x$ and $g(x)=x^2−1$

Word for word: Consider the functions $f(x)=\ln x$ and $g(x)=x^2−1$, find the domain and range of $(f\circ g)(x)$ I think this is asking to find the domain and range of $\ln(x)^{2}-1$ and the ...
1
vote
2answers
53 views

How to simplify the formula for $n$th Fibonacci number when $n=2$?

When n is equal to 2 how do I simplify when the $n=2$ is put into the equation below (by the way I have to prove this formula by induction that when n= any number it will equal that number) ...
2
votes
1answer
19 views

Which of the following relations are functions of q?

Firstly, what is a function of q? Am I correct to assume it means $f(q)$? $w=q+1$ For this one, it is a linear function, so it has to be a function of q. But I'm not sure how to express it? ...
2
votes
1answer
50 views

Simplifying a square root of a square

Simplify: $$(x^2+6x+9)^{-\frac{1}{2}} \cdot (x+3)^2$$ The answer is $x+3$, but I don't understand how? There is no restriction, should it not be as follows? $$\frac{1}{\sqrt{(x+3)^2}} \cdot ...
0
votes
0answers
20 views

Proof that the $sqrt[k]{z}\, z \in \mathbb N$ counts the amount of numbers less than or equal to z with a $k-$exact power

Empirically, it can shown that $$\mathrm{Floor}[\sqrt[k]{z} ] \,, z \wedge k\in \mathbb N $$ is equal to the amount of numbers which have a $k-$exact root. For example, $\sqrt 36 = 6$ means that there ...