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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1answer
20 views

Find total number of painted cubes

Suppose that a wooden cube, whose edge is 5 inch, is painted red, then cut into 125 pieces of 1 inch edge. Find total number of painted cubes ?
0
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1answer
15 views

Plug in numbers to find relationship between numbers

A total of k passengers went on a bus trip. Each of the n buses that were used to transport the passengers could seat a maximum of x passengers. If one bus had 3 empty seats and the remaining buses ...
3
votes
2answers
25 views

Piecewise linear function and absolute value

While writing a solution to homeworks for my students, I had to write the function $$f(x)=\left\{\begin{array}{ll} \frac{x+2}{2}, & x\leqslant -4\\ \frac{x}{4}, & -4\leqslant x\leqslant 4 \\ ...
1
vote
5answers
125 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.
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1answer
38 views

Solve an equation involving fractional powers

doing some BASIC programming, and have this exponential equation that works perfectly: Constants: $K=10,A=64,B=1023,D=1000$ The real variable input is $C\in[0,D]$ I have ...
2
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6answers
61 views

Adding $2$ absolute values together: $|x+2| + |x-3| =5.$

I came across a very basic absolute value question $|x+2| + |x-3| =5.$ Initially, I thought the answer was $x=-2$ and $x=3$ because I let each absolute values be either positive and negative and ...
1
vote
2answers
30 views

If two sides of an equilateral triangle measures $(6x+1)$ units and $\frac{11x+5}{2}$ units, find the perimeter of the triangle.

If two sides of an equilateral triangle measures $(6x+1)$ units and $\frac{11x+5}{2}$ units, find the perimeter of the triangle. I tried the following, Let the third side measure $x$ units ...
0
votes
5answers
129 views

Determine all solutions to $|x+12|+|x-5|=15$

Determine all solutions to the following. $$ \lvert x+12\rvert +\lvert x-5\rvert =15.$$ How can I solve problems like this? Should I try graphing the function? Should I somehow consider various ...
0
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2answers
32 views

How many boys, girls, men and women are there?

In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$. Solution: $b = g + 0.1g$--------(i), ...
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votes
0answers
13 views

Sharing and Distributing Surplus and Shortage Problem [on hold]

Allison, Beverly, and Christine have some pieces of chessmen. Half of Allison's chessmen and shared by Beverly and Chris equally, the half of Beverly's are shared by Allison and Chris equally. Lastly, ...
1
vote
1answer
10 views

Distributing Giving out Quarters Suplus and Shortage Problem

Amy, Betty, and Chloe have some quarters. Amy gives some of her quarters to Betty and Chloe, making their quarters doubled. Then Betty dos the same thing, making Amy and Chloe's quarters doubled. And ...
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2answers
72 views

Finding all solutions to the equation $|||||x|-1|-1|-1|-1|=0$

I was presented this question by a student I was tutoring: Suppose $x \in \mathbb{R}$. Find all solutions of the equation $$|||||x|-1|-1|-1|-1|=0.$$ What I explained to the student: Given ...
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votes
4answers
40 views

Physics problem, stuck in algebra.

I end up with the equations; $$u=u_1' \cos(a)+u_2' \cos(b)$$ $$u_1' \sin(a)=u_2' \sin(b)$$ $$u^2=u_1'^2+u_2'^2$$ I have to show that $$a+b=\frac{\pi}{2}$$ $x'$ isn't the derivative of $x$, it's a ...
-1
votes
1answer
43 views

Solving system of equations with complex numbers

Equation 1$$ \frac{V_{1}}{5} + \frac{V_{1}-V_{2}}{10+j6} - 10\angle45^\circ = 0 $$ Equation 2 $$ -4V_{1} + \frac{V_{2}-V_{1}}{10+j6} + \frac{V_{3}}{-j2} + \frac{V_{3}}{8+j7} = 0 $$ Equation 3 $$ ...
4
votes
4answers
189 views

Finding $\frac{\mathrm d}{\mathrm dx} x!$

I'm trying to differentiate $x!$ but I just can't seem to do it right. I define the function as follows: $$x! = \prod_{r = 0}^{x}(x-r) \quad,\quad x \in \mathbb N$$ I've tried attempted to try it by ...
-1
votes
3answers
27 views

Find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

Find the slope-intercept form of the equation of the line passing through the points. Sketch the line. (-8,1),(-8,7) (-1,4),(6,4) Progress The slope that I get for number 1 is ...
0
votes
0answers
31 views

A Discount equation. [on hold]

I am have trouble remembering how to do a discount equation that it will not give more than $40\%$. So if I say I sell more than $1$ of the product it will decrease by a percentage, but it will only ...
0
votes
1answer
1k views

Question about transform on digits

I need help with a problem. Forvany positive integer m, let u be its units digit and t be it's number to tens, that is, the integer obtained when u is removed from m. So m=10t+u. For any positive ...
0
votes
1answer
59 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 ...
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4answers
39 views

Find algebraic function to describe number of people “x”

For a group of x people, Joe ordered 5 pizza pies, each of which was cut into 12 slices. Each person was originally supposed to have an equal number of slices. However, four people did not want any ...
14
votes
3answers
185 views

Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
2
votes
5answers
113 views

Why can't I find any solution of this three equations?

$$2x+6y-z=10$$ $$3x+2y+2z=1$$ $$5x+4y+3z=4$$ I do not find any solution of this three equations.I know that if two equations or planes are parallel then we do't find any solution.But I can't ...
0
votes
1answer
38 views

First degree or second degree quadratic equation?

$X-\sqrt{121}= 0$ $Y^2-121=0$ When I try to solve by squaring on both sides the first equation changes to $X^2-121 =0$, where $x = \pm 11$. When I try to solve it this way: $x= \sqrt{121} = +11$, ...
2
votes
6answers
104 views

Tangent to $e^x$

I have been asked to find the tangent to $y=e^x$ that passes through origin. This is what i came up with. Tangent $f(x)=e^x(x-a)+f(a)$, where a is zero, I therefore conclude with $e^xx$ to be the ...
32
votes
2answers
1k views

Find all real numbers $x$ for which $\frac{8^x+27^x}{12^x+18^x}=\frac76$

Find all real numbers $x$ for which $$\frac{8^x+27^x}{12^x+18^x}=\frac76$$ I have tried to fiddle with it as follows: $$2^{3x} \cdot 6 +3^{3x} \cdot 6=12^x \cdot 7+18^x \cdot 7$$ $$ 3 \cdot ...
0
votes
3answers
48 views

The $n^{th}$ root of $1$

How do I prove that the $n^{th}$ root of $1$ forms the vertices of a unit $n$-gon in the complex plane? For example when I graph the $3$ solutions of $\sqrt[3]{1}$ they form the vertices of a unit ...
4
votes
1answer
61 views

Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$?

The exercise asks me this: Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$? ps: $f: \mathbb{R}\to \mathbb{R}$ I really don't know how to start :c, I appreciate hints.
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0answers
36 views

Reverse engineer applying fees

So I am having an interesting problem that I am unable to solve. Let me just start by saying I know absolutely nothing about math but that doesn't stop me from trying to solve this equation in the ...
4
votes
4answers
193 views

Alternative ways to solve this trigonometric inequality?

The inequality is: $$ \frac{\sin{\theta}+1}{\cos{\theta}}\leq 1 \text{ with } \cos{\theta}\neq0 \land 0\leq \theta\lt 2\pi$$ I've tried splitting it up into cases of $\theta$ that make ...
0
votes
3answers
47 views

Horse Betting Odds - But Guaranteed Win!

Suppose four horses - $A, B, C$, and $D$ - are entered in a race and the odds on them, respectively, are $6$ to $1$, $5$ to $1$, $4$ to $1$, and $3$ to $1.$ If you bet $\$1$ on $A$, then you receive ...
22
votes
6answers
746 views

If $(\sqrt{y^2-x}-x)(\sqrt{x^2+y}-y)=y$ then $x+y=0$.

Let $x,y$ be real numbers such that $$\left(\sqrt{y^{2} - x\,\,}\, - x\right)\left(\sqrt{x^{2} + y\,\,}\, - y\right)=y$$ Show that $x+y=0$. My try: Let ...
-1
votes
3answers
75 views

The sum of the $n$ smallest odd numbers is equal to $n^2$ [duplicate]

if given a positive integer $n$ is the sum of the $n$ smallest odd numbers equal to $n^2$
0
votes
1answer
219 views

Reverse a formula with codependent expressions

I apologize for my title, but I really am a long way from understanding how to even describe my problem accurately, let alone solving it. I'm looking to reverse this formula: ...
3
votes
2answers
80 views

The juice-problem

I have got an exercise. 7 men are in a room, sitting at a table. In front of each people is a cup. In some cups are juice. The cups altogether have got 3 liters juice in them. Now the first man pour ...
0
votes
4answers
66 views

perpendicular bisector of AB

Let $A(-6,9)$ and $B(10,-3)$ be points in the plane Find an equation of the perpendicular bisector of $AB$ the answer I get is $y=(4/3)x+(1/3)$ but it is not correct.
1
vote
2answers
339 views

If an AP, a GP and a HP have the same first term and same $(2n+1)$th terms and their $n$th terms are $a,b,c$ respectively

If an arithmetic preogression, a geometric progression and a harmonic preogression have the same first term and same $(2n+1)$th terms and their $n$th terms are $a,b,c$ respectively, then find the ...
1
vote
1answer
33 views

Trigonometric inequality question [on hold]

Let $0 < A < \frac {\pi}{2}$ and $0 < B < \frac {\pi}{2}$. (a) prove that $\sec^2 A + \csc^2 A \cdot \csc^2 B \cdot \sec^2 B \geq 9.$ (b) determine values of $\sec A$ and $\sec B$ when ...
0
votes
2answers
30 views

Conversion of dosage based on body weight

Infant ibuprofen containes 100mg/5.0mL suspension. The recommended dose is 10mg/kg body to weight. How many mL of this suspension should be given to an infant weighing 18 lb? That's not a serious ...
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votes
1answer
25 views

Completing the square, optimizing [on hold]

Express the quadratic function y=-3x^2+18x-3 in the form of y=a(x-p)^2+q. Hence determine the maximum or minimum point of the function.
1
vote
6answers
66 views

Graph of the $\sqrt { x } $

Why does the graph only go to the right and up? Wouldn't there be negative values of y as well? Since, for example, the $\sqrt{4}$ is $2$ and $-2$
0
votes
2answers
22 views

Question about the graphs of functions

If the point $(2,3)$ is on the graph of $f$, then what can we say about $f(2)$? I have an idea of what this question is asking me but nothing more. I suspect that it has something to do with linear ...
2
votes
4answers
43 views

Simplifying/solving a logarithm $\log_24^{2n}$

Need help with simplifying this logarithm. $$\log_24^{2n}$$ Would I just pull the 2n to the front: $$2n*\log_24$$ So it would simplify to $$4n$$ Is this correct or am I completely wrong?
0
votes
2answers
24 views

How to find the slope of a secant line of the graph of a function?

The point $P(5,-2)$ lies on the curve $y=\large\frac{2}{4-x}$. (a). If $Q$ is the point $(X,\large\frac{2}{4-x})$, find the slope $M_{pq}$ of the secant line $PQ$ (correct to six decimal places). ...
0
votes
1answer
25 views

Logistic population: determine parameter $r$

The general forumla for a logistic population is: $$ P_{n+1} = P_n + r*P_n*(1-\frac{P_n}{K}) $$ I was given $P_{12} = 95.75$ and $P_{14} = 98$, as well as $K = 100$. To solve for $r$, I decided to ...
2
votes
4answers
39 views

Complete the squares to find the center and radius of the circle

I've had trouble on this one problem for a couple days. Complete the square on the X and Y terms to find the center and radius of the circle. $x^2+2x+y^2-4y=-4\:\:$
2
votes
3answers
28 views

Help with finding a vertex

I am having trouble with this math problem. The coordinate of the vertex of $f(x) = ax^2 + bx +c, a \ne 0$, is______. Now I know that to find the $x$ coordinate I would use this formula. $x = ...
0
votes
1answer
154 views

Getting a number from interest equation

Here is the question for my homework: A mother wants to invest $\$7000.00$ for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns ...
-1
votes
2answers
3k views

Converting a radical to a mixed radical

Say I have $\sqrt{\frac{2}{9}}$. How would I convert this to a mixed radical where the radicand is a whole number? I can convert the $\sqrt{8}$ to a mixed radical easily, $2\sqrt{2}$, but this ...
3
votes
3answers
242 views

$\$10$ and $\$100$ bill equation

My question: A cashier has a total of $114$ bills, made up of tens and hundreds. The total value of the money is $\$6450.00$. How much of each kind does he have? He has [BLANK] tens and [BLANK] ...
2
votes
5answers
398 views

Help with a proof: Given $a\ne 0$ and $b\ne 0$ and $a \lt \frac{1}{a} \lt b \lt \frac{1}{b}$. Prove $a\lt -1$

This question is from the book How to Prove It and I'm having trouble getting started with it. The book provides the hint "first prove $a \lt 0$". However, I can't figure out how to get that far with ...