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)

-5
votes
2answers
17 views

Ticket price word problem - Simultaneous equations

Jen has been pricing speed-pass train fares for a group trip to NY. Three adults and four children must pay $\$101$. Two adults and three children must pay $\$71$. Find the price of the adults ticket ...
-1
votes
1answer
22 views

Exponential Function Equation and inverse Pre-Cal

I am not completely sure if I wrote the equation correctly. For A I wrote: m(t)=100(b^x) Not sure it is correct...but how do I find the inverse? That doesn't make sense to me. Do I use log?
1
vote
4answers
30 views

Logarithm Question (Find x)

How to solve x for $$x^{2\log_{10}x}=\frac{x^5}{100}$$?
0
votes
1answer
25 views

Use the remainder theorem to find $P(2)$ where $P(x)=-x^4+3x^3-4x+7$

Use the remainder theorem to find $P(2)$ where $P(x)=-x^4+3x^3-4x+7$ Quotient = ? Remainder = $P(2)$ = ?
0
votes
2answers
25 views

Solution set of inequality

This is the question: $$\frac{1-2x-3x^2}{3x-x^2-5} \gt 0$$ What I did : I got the answer as $$\left(x-3\right)\left(x+1\right) \gt 0$$ giving me the solution set : $x \in (-\infty,-1 ...
4
votes
5answers
640 views

My dilemma about $0^0$ [duplicate]

We know that $0^0$ is indeterminate. But if do this: $$(1+x)^n=(0+(1+x))^n=C(n,0)\cdot ((0)^0)((1+x)^n) + \cdots$$ we get $$(1+x)^n=(0^0)\cdot(1+x)^n$$ So, $0^0$ must be equal to $1$. What is ...
-2
votes
1answer
35 views

Find minimal $x$ and $y$ that creates $4$ [on hold]

Hello I had this in my exam, I've never studied this and I am interested in knowing how to solve it, and what is the category of this type of question: For all positive numbers $x$ and $y$ such that ...
0
votes
0answers
16 views

Expansion $(x_1+x_2+\dots+x_m)^p\,(y_1+y_2+\dots+y_n)^q$?

Based on multinomial series, we have $(x_1 + x_2 + \cdots + x_m)^p = \sum_\limits{k_1+k_2+\cdots+k_m=p} \frac{p!}{k_1!\, k_2! \cdots k_m!} \prod_\limits{1\le t\le m}x_{t}^{k_{t}}\,$. So what is ...
1
vote
2answers
44 views

$y=\cos(m \arcsin x)$ Validity of solution $\dfrac {dy} {dx}$ when $x=0$?

$y=\cos(m \arcsin x)$, for $ -1 < x < 1$ I want to find the value of $\dfrac {dy} {dx}$ when $x=0$ using the following way: $=> \arccos y = m\arcsin x$ $=> - \dfrac {1} {\sqrt {1-y^2}} ...
0
votes
0answers
11 views

are $g$, $f$ terms of equation of a circle different from that in the general equation of second degree?

I know the conditions for a general equation of second degree $$ax^2+by^2+2hxy+2gx+2fy+c=0$$ to be a circle are 1. $h=0$ 2. $a=b$ So following the conditions the equation becomes ...
1
vote
1answer
14 views

Formula to map a variable to another?

For example, I have a variable $x$ that contains the value $100$, and assume I also have a variable $y$ that contains the value $300$ is there a method to decrement $x$ by some amount and have $y$ be ...
2
votes
1answer
26 views

If $(a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2 = 0$ are real and distinct, Then set of all values of $a$

If the two roots of the equation $(a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2 = 0$ are real and distinct, Then the set of all values of $a$ is. $\bf{Options::}$ $(a)\;\; \displaystyle ...
-2
votes
2answers
26 views

Use the fundamental identities to simplify the expression. [on hold]

Use the fundamental identities to simplify the expression $$ 4 \sin x (\csc x - \sin x) $$
0
votes
0answers
26 views

Help understanding exponential formula

I am reading a paper in which a group is approximating data that fits an exponentially declining curve. They use the following formula to fit the data, where τ is the y-axis variable and v is the x ...
3
votes
3answers
63 views

How various properties of numbers, operations are found?

I know that how the term "property" is defined. Definition: An attribute, quality, or characteristic of something. Like one of the property of addition is "commutativity" which behaves like, ...
0
votes
3answers
34 views

Algebraic Manipulation

What is the best method to get the LHS equal to RHS? $\frac{n(n+1)(n+2)}{3} + (n+1)(n+2) = \frac{(n+1)(n+2)(n+3)}{3}$ Thank you.
0
votes
1answer
63 views

Simplify $(x_1+x_2+\dots+x_m)^p$? [duplicate]

Is there a way to simplify $(x_1+x_2+\dots+x_m)^p$? Thank you!
0
votes
1answer
37 views

Algebra question leading to a 3rd order equation solving.Any other answers?

if : $x+y+z=2$ , $ x^2+y^2+z^2=3$ , $xyz=4$ Then evaluate: $\frac {1} {xy+z-1} + \frac {1} {yz+x-1} + \frac {1} {zx+y-1}$ My try: $(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+xz)=4 \rightarrow 3+2(xy+yz+xz)=4 ...
1
vote
1answer
33 views

Real Numbers are Roots $r, s$.

Real numbers $r$ and $s$ are roots of $p(x)=x^3+ax+b$, and $r+4$ and $s-3$ are roots of $q(x)=x^3+ax+b+240$. Find the sum of all possible values of $|b|$. Using Vieta's Formulas, $r+s+x_1$ $=0$ ...
1
vote
2answers
17 views

The sum of the abscissae of the intersections of a cubic and a line

I remember being told in passing in a talk once the following theorem: Let $y=x^3$, and let $x_1,x_2,x_3$ be the abscissae ($x$ co-ordinates) of three distinct points on this cubic. Then ...
-5
votes
0answers
28 views

Question about alpha and beta [on hold]

If $\alpha$ and $\beta$ are zeroes of polynomial $4x^2-3x+8$. find the value of $\alpha^2-\beta^2$.
2
votes
3answers
29 views

Make $kt^2+(3k+1)t+4k+1$ constant?

Find $k$ such that $kt^2+(3k+1)t+4k+1=0$ is an identity (i.e. true for all $t$). E.g. $k=t+1$ doesn't work since you end up with a third degree polynomial in $t$ which determines $t$, making $t$ ...
-1
votes
4answers
53 views

Multiplying whole number with fractions.

I'm looking at a solution to a math problem and there are obviously some rules regarding multiplication of fractions that I don't know. Can someone make any sense of this? $$s_n = 625 \cdot ...
1
vote
2answers
20 views

Absolute Value Algebra with inverses

I noticed the following equality in some material regarding limits and infinite series. $$ \left |\frac{x}{x+1} - 1 \right| = \left |\frac{-1}{x+1} \right| $$ And I'm honestly stumped (and slightly ...
2
votes
4answers
35 views

Simultaneous Quadratic Equations: $x^2 + y ^ 2 - 2 x + 6y - 35 = 0$ and $2x + 3y = 5$

I've been given the task to simultaneously solve: $$x^2 + y ^ 2 - 2 x + 6y - 35 = 0$$ $$2x + 3y = 5$$ I've tried applying the substitution method by reordering the second equation to both $x$ and ...
1
vote
4answers
58 views

Proving by induction that $n^2 - 7n - 2$ is divisible by $2$

Now proving by induction is fairly simple. However, this is a multiple choice problem whose answers don't make any sense to me. The actual problem goes as follows: To prove by induction that $n^2 - ...
1
vote
1answer
33 views

Find the volume of the region bounded by $ (x^{2}+y^{2}+z^{2})^{2}=x$

I tried to convert it to spherical coordinates to find the bounds: $(p^{2})^{2} = p\sin(\phi) \cos(\theta)$ => $ p^{3} = \sin(\phi)\cos(\theta)$ not sure where to go from here.. $ 0 < \theta ...
0
votes
3answers
31 views

Algebra rearranging

I'm stuck on a question that should be extremely easy. The idea is to show that $$\frac{\frac{n}{z}y + a}{y + \frac{z}{n}a} = \frac{n}{z}$$ What is the best method here? Thanks
0
votes
0answers
35 views

Help: Studying A-Level Mathematics [on hold]

Although I am a latecomer at the age of 21 years of age, I have enrolled in self taught mathematics A-level with "Edexcel" both mathematics & further mathematics. I am in need of help with ...
1
vote
1answer
42 views

Simple Logarithmic question.

I was just wondering if i can do this. Q. Solve $\log_{9}24=x $ $\implies9^x =24$ $\implies3^{2x}=2^3 3$ $\implies\log_3(3^{2x})= \log_3(2^3 3)$ $\implies2x=2 (3)^{1/3}$ $\implies x=3^{1/3} $ ...
0
votes
0answers
25 views

Complex Geometry Problem

Let $A_1 A_2 \dotsb A_{11}$ be a regular 11-gon inscribed in a circle of radius 2. Let $P$ be a point, such that the distance from $P$ to the center of the circle is 3. Find [$PA_1^2 + PA_2^2 + \dots ...
-1
votes
1answer
51 views

Determine $x+y$ when equalities involving higher powers are given. [on hold]

Let $x$ and $y$ be rational numbers, such that $$\begin{cases} xy&=&\dfrac{128}{33^2}\\\\x^5+y^5&=&2x^2y^2 \end{cases}$$ What is $x+y$? Thanks in advance.
-5
votes
0answers
43 views

Find positive solutions to $\frac{(x+y+z)(xyz+4)}{xyz}=9$ [on hold]

Find positive solutions to $\frac{(x+y+z)(xyz+4)}{xyz}=9$. Thanks in advance.
2
votes
3answers
237 views

Geometry with complex numbers.

Let $a$, $b$, $c$, and $d$ be four complex numbers on the unit circle, such that the line joining $a$ and $b$ is perpendicular to the line joining $c$ and $d$. Find a simple expression for $d$ in ...
3
votes
3answers
63 views

How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$

I know there are many methods to scale a number from range $[A,B]$ to a range $[C,D]$, and I've searched over and over the web. I've seen this math.SE thread. I need to scale a big number (signed ...
0
votes
2answers
25 views

Converting log form of equation into linear form

I am trying to convert part of an equation from its log form into a linear form. Specifically, I am trying to convert $10^{4 log (x)}$, into $x^4$, but I'm really unsure of how to get from this first ...
1
vote
1answer
23 views

Are $a/3, b/3$ equivalent to $1/3(a), 1/3(b)$

I have the following expression with two answers, I'm not sure if they're correct: $1/3(a+b) = 1/3 (a) + 1/3 (b)$ can the answer be: $a/3+ b/3$ too?
1
vote
2answers
40 views

Inverse function.

A function $h$ is defined by $h:x\rightarrow 2-\frac{a}{x}$, where $x\neq 0$ and $a$ is a constant. Given $\frac{1}{2}h^2(2)+h^{-1}(-1)=-1$, find the possible values of $a$. Can someone give me some ...
0
votes
1answer
18 views

Something is not adding up here? Intersection of curves.

I'm doing a 'basic' problem on the intersection of curves as part of a larger question, but something isn't quite adding up! I'm trying to find the point of intersection of $y=\frac{1}{k}x(1-x)$ and ...
1
vote
3answers
31 views

Verbal question problem help

I had this question today and I got confused on how to construct my solution for this. At the first view of the question, I decided to use $X$ and $Y$ and no other option: Maria purchased $X$ books ...
-1
votes
0answers
35 views

Algebra fraction simplification? [on hold]

I have the following and is solution but I don't understand how they arrived at the solution.Can someone direct me to how they arrived at this please ? $$\frac{z(z-1)(z+1)}{(z-3)^3}$$ The solution : ...
0
votes
2answers
55 views

how to convert log(x) into linear form? [on hold]

I have simple function which is non-linear like log(x) I want to convert it into linear function. Anyone could help out? Thanks
0
votes
2answers
34 views

Can a equation be represented by more than one graph of different dimensions

Consider the equation $x^2 + y^2 - 0z = 1$ If you only consider the x-y plane, this will trace out the well-known unit circle. However, if you consider 3d space, a cylinder of infinite height without ...
3
votes
1answer
39 views

Finding all possible pairs of positive integer values

The ratio of the sum of two positive integers to their difference is $7:5$. If the the sum of the two numbers is at most $25$, find all possible values for the pair of numbers. Let $m$ be the first ...
0
votes
1answer
29 views

Are these two definitions of an affine subspace equivalent?

I've seen the notion of an affine subspace defined differently as follows: $S \subset \mathbb R^3$, non-empty, is an affine subspace if $(1-t)u + tv \in S$ whenever $u,v \in S$. $S$ is an affine ...
-2
votes
0answers
17 views

Calendar question [on hold]

A certain day, which is $x$ days before $17$th of August is such that $50$ days prior to that day it was $4x$ days since March $40$th of the same year. What is $x$?
-3
votes
1answer
68 views

Do you agree with this!

So yeah, I stuck with this theory. I thought -4 Square = 16
0
votes
1answer
29 views

Transpose exponential equation [on hold]

Could somebody please help with transposing the following equation to isolate x to the left side of the equation to solve for x? $$ y = 10^{1.830 \log(x)} + 2.686 $$
-2
votes
0answers
22 views

What is the difference between the middle factor and the middle term of permutation ? [duplicate]

What is the difference between the middle factor and the middle term of permutation ?
0
votes
1answer
22 views

Simple Harmonic Motion Formula

The SHM general formula is this: $y(t) = A\sin(\omega t + \alpha) +B$ I have two questions about it As far as I know, there is the cosine formula for when the particle starts at P and sine for ...