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
votes
1answer
25 views

If $5x/(2x^2+5x+1)=1/3$ then the value of $ (x+1/2x)$ is

If $5x/(2x^2+5x+1)=1/3$ then the value of $ (x+1/2x)$ is note 5x=1 2x^2+5x+1=3 or 15x=2x^2+5x+1 so 2x^2-10x+1 so (5+sqrt(23))/2 or (5-sqrt(23))/2
1
vote
2answers
48 views

If the equation $2x^2-7x+12=0$ has two roots alpha and beta ,then the value of alpha/beta+beta/alpha is

If the equation $2x^2-7x+12 =0$ has two roots $\alpha$ and $\beta$ , then the value of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$ is note $x=\frac{-7+\sqrt{47}}{4},\frac{-7-\sqrt{47}}{4}$ then ...
3
votes
1answer
29 views

If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is

If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is...
1
vote
1answer
24 views

How much above the cost price must he marks his goods above the cost price to make a profit of 17%

A businessman allows a discount of $10$% on written price. How much above the cost price must he mark his goods to make a profit of $17$% ? note: $x\times\frac{90}{100}=x\times\frac{117}{100}$ ...
0
votes
1answer
26 views

In how many days $Y$ alone finish the work

$X$ and $Y$ do a piece of work in $30$ days .They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days.In how many days $Y$ alone finish the work. note:$X+Y=1/30$ ...
0
votes
1answer
16 views

A math question related to creating a risk formula..

If I'm not using correct terminology, or this isn't clear, I will gladly edit/clarify. I'm trying to figure out how to create method or formula(s) to produce a score based on 4 variables, all real ...
1
vote
1answer
23 views

Simplifying a product written in Capital Pi Notation

I'm having some trouble figuring out how to simplify Capital Pi Notation. What I tried was to expand the multiplication with various n and tried to find a pattern. Could someone point me in the ...
0
votes
1answer
22 views

How do I multiply $2(\frac{4}{y})$?

How do I multiply $2(\frac{4}{y})$? I'm having abit of trouble understanding how the answer is 8y...
1
vote
2answers
43 views

Find the equation for the circle

Find an equation for the circle that has center $(−3, 4)$ and passes through the point $(4, −2)$ I keep getting $(x+3)^2+(y-4)=113$
4
votes
2answers
18 views

Condensing Fractional Logarithms

Does the following condense to the following: $\log_2z+(\log_2x)/2+(\log_2y)/2 = \log_2(z\sqrt{x}\sqrt{y})$ or to $\log_2(z\sqrt{xy})$ ?
3
votes
3answers
68 views

Rationalize the denominator and simplify

So the problem I have says rationalize the denominator and simplify. $$ \frac{ \sqrt{15}}{\sqrt{10}-3}$$ My answer I got was $\frac{5 \sqrt6}{7}$. Am I doing this wrong or is this the wrong ...
-1
votes
3answers
70 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
29 views

Quadratics help please [on hold]

Does it matter when you are solving quadratics and you get an or would it matter if you said does x always go first $x<9$ or is it the same as $9<x$?
11
votes
3answers
259 views

What happens to a function when it is undefined?

If I have the function $$f(x) = {x^2 - 2 \over x + \sqrt 2}$$ this is undefined for $x = -\sqrt 2$, am I correct? Since the denominator would be zero. But the numerator is a difference of ...
0
votes
2answers
45 views

Finding equations with known roots

I have the equation .The roots are a, b ,c. How can I find another equation whose roots are without using Vieta??
0
votes
2answers
34 views

How would I solve this for the indicated variable?

$a^{ 2 }x+(a-1)=(a+1)x$; for $x$ I have been able to manipulate and solve for the indicated variable in these type of equations pretty easily until I came across this one. I know that I have to ...
1
vote
2answers
32 views

Proof of logarithmic identity $\log_g x=\log_a x\cdot\log_g a$

I have to prove the alleged link between the logarithms in base g and a $$\log_g x=\log_a x\cdot\log_g a$$ I know that this can be written as: $$\frac{\ln x}{\ln g}=\frac{\ln x}{\ln g}$$ But does ...
0
votes
1answer
17 views

Calculate Growth rate of one day

I was given that a population doubles in 4.8 days. Now I need to calculate the growth rate of one day. This question is in the topic of the Malthus model. To get the intrinsic growth rate: birth rate ...
0
votes
2answers
40 views

process of summing series [on hold]

I'm trying to solve the following exercises, but I have a difficulty: a) Find the sum of the telescoping series : b) Find the sum of this series :
0
votes
1answer
41 views

Simplify the expression $(2x^2 - 2)/(x+1)$ to 2x + 2

So I want to Simplify the expression $(2x^2 - 2)/(x+1)$. I've used wolfram alpha and even looked up the answer witch is 2x + 2. But I totaly forgot how! (I know it's pretty simple I have just ...
2
votes
1answer
11 views

Exponential Form Conversion

Does $(\sqrt[3]{3k})^4 = (3k)^{4/3}$ or $((3k)^{1/3})^4$? I thought the first one is correct, but when I looked at it again I saw that $(3k)^{4/3} = \sqrt[3]{(3k)^4} $
0
votes
1answer
19 views

Expressing a solution in interval notation

I am faced with this problem. I am told to express the answer in interval notation. |3x| > 12 I solve like usual, by doing this: ...
0
votes
0answers
35 views

Mortgage bond monthly repayment

I was given the following question: A mortgage bond of 280000 is taken out on a house at a rate of 19.25% p.a., compounded monthly over 25 years. Question: Calculate the monthly payment ...
3
votes
6answers
132 views

Why is $0/0$ not $\Bbb R$? [duplicate]

Whenever I asked my grade school and college teachers why $\frac00$ is undefined, they would show me a graph of $\frac1x$ and point out the vertical asymptote at $0$, noting that "Since it approaches ...
1
vote
2answers
33 views

Expressing $ 12\sin( \omega t - 10) $ in cosine form

$$ 12\sin( \omega t - 10) $$ I understand how it's solved when using the graphical method, however I'm having trouble understanding something about the trigonometric identities method. The solution ...
-7
votes
0answers
42 views

Solving a system of polynomial equations in three variables (x^2-yz=18, y^2-zx=8, z^2-xy=-7)

Solving a system of polynomial equations in three variables (x^2-yz=18, y^2-zx=8, z^2-xy=-7 I've tried rearranging each equation to isolate for one variable ex: z^2-xy=-7 --> z= x^2-18/y after, I ...
1
vote
1answer
25 views

Show that the value of $\frac{\text{d}^{2r+1}y}{\text{d}x^{2r+1}}$ when $x=0$ is $\frac{1}{2^{2r}}\left(\frac{(2r)!}{r!}\right)^2$

The question originally asks you to prove that if $y=\sin^{-1}(x)+(\sin^{-1}(x))^2$ that: $(1-x^2)y''-x y'$ is independent of $x$. I get that $(1-x^2)y''-x y'=2$ hence proving the first part. The ...
0
votes
1answer
33 views

Speed and distance formula derivation [on hold]

if two persons start at the same time from two points a and b towards each other, and after crossing they take x and y hours in reaching b and a respectively then a's speed : b's speed = $\sqrt y : ...
-2
votes
0answers
26 views

System of three quadratics in three unknowns [on hold]

$$x^2-yz=18,y^2-zx=8,z^2-xy=-7$$ Please solve each variable and SHOW YOUR WORK (please)! :-)
0
votes
1answer
37 views

How would I test this equation for symmetry?

$$x^{ 2 }y^{ 2 }+xy=1$$ I know the procedures to test for symmetry with respect to the x axis, y axis, and origin... but I think that I wouldn't be able to do that here without first manipulating the ...
-6
votes
2answers
37 views

Use the numbers 1, 2, 3, 4 to equal 7 [on hold]

We need to add, subtract, or multiply 1,2,3,4 to equal 7. Ex. (2+3)-(4*1)= 1 5-4=1
1
vote
1answer
37 views

Quadratic equations - finding value of x

Question: Solve the equation $$\frac{2x}{3x^2 - x+2} - \frac{7x}{3x^2 + 5x+2} = 1$$ I attempted to split the two quadratic equations into their roots, however, was unable to do so. Then I tried to ...
3
votes
2answers
352 views

How would I find a point on the y-axis equidistant from two other points?

The points are$$(5,-5) and (1,1)$$ I tried doing this visually and came up with (0,-5). This wasn't correct once I applied the distance formula to check the distance between that point and the two ...
2
votes
4answers
52 views

Quadratic equation - solving for x

Question: Solve the equation $$(x+2)(x+3)(x+8)(x+12) = 4x^2$$ I tried to solve the equation by expanding the LHS and then equating it to the RHS, but that just doesn't seem to be feasible. I am ...
1
vote
1answer
16 views

How to solve t-distribution f0r standard deviation?

I am currently refreshing my statistics knowledge and I am struggling with simple algebra (sad, but true...). Consider the t-formula: $$\text{Interval} = \bar X \pm ...
0
votes
2answers
28 views

Solving an absolute value inequality with a negative?

$$8-|2x-1|\ge 6$$ I watched the Khan Academy video on absolute value inequalities, however I still don't understand what I would do in this situation with the $$8-$$ in front of it. Taking what I ...
0
votes
0answers
13 views

formula required when given a net result to calculate the gross number [on hold]

Net result or answer is 725,000 Trying to find a formula to calculate the price needed to be obtained given; Commission is charged at 5% on the 1st 18,000 and 2.5% on the balance tax of 10% is then ...
1
vote
2answers
26 views

Rearranging equation $t = \frac{T}{2\pi} (\psi - \epsilon \sin \psi)$ in terms of $\psi$

I was playing around with the maths for orbits and trying to make a parametric equation that, well.. worked. I found a worksheet with parametrics with another variable ($\psi$), but I wanted to be ...
0
votes
1answer
18 views

Solving $\frac12 (3y+2)-\frac58=\frac34y$ for $y$ using LCD method

I am solving $$\frac12 (3y+2)-\frac58=\frac34y$$ for $y$ using LCD method. Can't figure out what I did wrong! The answer in the back of the book is $-1/2$. PS: In the first line that is a $1/2$ in ...
0
votes
0answers
10 views

Function Transformation of the following:

Is the following correct? $f(x) = 2x-1$ ----> $g(x) = f(-x)$ -----> $g(x)= -2x-1$ and $f(x) = \sqrt{x+3}$ -----> $g(x)=-f(x)+1$ ----> $g(x)=-\sqrt{x+3}+1$ and $f(x)=2^x$ ---->$g(x)= f(x)-4$ ...
0
votes
1answer
33 views

How to solve $\lambda(xyz)^p= (xy)^p$ [on hold]

I thought $\lambda = 1/{z^p}$ but that isn't correct. Any help greatly appreciated.
3
votes
0answers
36 views

Writing sum of square roots with symmetric polynomials

I want to write the function $$ F_N=\sum_{i=1}^N\sqrt{x_i} $$ in terms of the $N$ elementary symmetric polynomials of the $N$ positive variables $x_1,\dots,x_N$. The $N=1$ case is trivial, as we ...
0
votes
1answer
28 views

How to graph the following square root function

How would you graph $f(x) = \sqrt{a^2 +x^2}$ ? What does the "a" mean in the equation?
1
vote
2answers
44 views

How to find roots for $y = ||x^2-x-20|-8|$

$$ y = ||x^2-x-20|-8| $$ After I set $y = 0$, I do not know how to deal with multiple absolute values.
1
vote
2answers
28 views

Translate the word phrase into a variable expression? [on hold]

Eight less than the quotient of $x$ and $3$. A. $3x-8$ B. $\dfrac{x}{3} - 8$ C. $\dfrac{x-8}{3}$ D. $\dfrac{8-x}{3}$
1
vote
3answers
150 views

Stuck solving a nonlinear inequality

$$\frac { x+2 }{ x+3 } <\frac { x-1 }{ x-2 } $$ This is what I got so far: $$\frac { x+2 }{ x+3 } -\frac { x-1 }{ x-2 } <0$$ Now I am completely lost because I don't know the next step. This ...
1
vote
3answers
49 views

$\ln (2 x-5)>\ln (7-2 x)$

Solve $$\ln (2 x-5)>\ln (7-2 x)$$ The answer is given as $$3<x<7/2$$ This is what I have done $$\ln (2 x-5)-\ln (7-2 x)>0$$ $$\ln \left(\frac{2 x-5}{7-2 x}\right)>0$$ However I am ...
0
votes
1answer
23 views

Use the Laws of Logarithm to expand: $4\log(x)- \frac{1}{3}\log(x^2+1)+2\log(x-1)$

For this question I got $$\log \Biggl(\frac{x^4}{(x^2+1)^{1/3}(x-1)^2}\Biggr)$$ However, the answer key in the book has $(x-1)^2$ in the numerator. Why?
0
votes
2answers
21 views

Expand the Expression: $\log\left({(x^2+4)^{1/2}}/\left\{(x^2+1)(x^3 - 7)^2\right\}^{1/2}\right)$

Expand the expression: $$\log\frac{\sqrt{x^2+4}}{\sqrt{(x^2+1)(x^3-7)^2}}$$ I got $$\frac{1}{2}\biggl(\log(x^2+4)-\log(x^2+1)+2\log(x^3-7)\biggr)$$ but the answer key says: ...
-6
votes
1answer
45 views

fund raiser question solve it please [on hold]

The population of an island is 500. To raise funds, a club organized a netball match. The event raised 300000 RF. Tickets were priced as follows RF 748 for males RF 712 for ladies RF 45 for kids How ...