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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1
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4answers
26 views

Number of distinct real roots with $e^{-x}$ in the equation

How to find the number of distinct real roots of the equation $$13x^{13}-e^{-x}-1=0$$ I know that we generally find number of real roots by observing number of sign changes in $f(x)$ and $f(-x)$ but ...
0
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2answers
15 views

Do you use the inner or outer degrees of a right-angled triangle when calculating the vertical component of a vector

I'm given the assignment of finding the vertical component of vector a - b. Below is an image of vector A. ||A|| = 6. I need to calculate side y. I was following the assignment and tried solving y ...
0
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0answers
19 views

why does a polynomial with square values work like this?

If $q(x)$ is a polynomial and $q(n)$ is a square for all integers $n\geq n_0$, then $q(x)$ is square of a polynomial.
1
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2answers
79 views

Evaluation of $\int\frac{\sqrt{\cos 2x}}{\sin x}dx$

Evaluation of $$\displaystyle \int\frac{\sqrt{\cos 2x}}{\sin x}dx$$ $\bf{My\; Try::}$ Let $\displaystyle I = \int\frac{\sqrt{\cos 2x}}{\sin x}dx = \int\frac{\cos 2x}{\sin^2 x\sqrt{\cos 2x}}\sin xdx ...
0
votes
1answer
20 views

Using $\pm$ to express “in the range of” statement.

Does it make sense to write: $x = \left\{A\pm B\right\}$ To mean that $x$ falls in the range of $\left\{A-B,A+B\right\}$? If not, what would be the correct way of expressing this? Many thanks!
3
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2answers
62 views

An inequality I am stuck on

This is somehow related to this problem but I don't have any idea about it. $a,b,c,d$ are positive reals such that $a+b+c+d=4$ $$\frac{1}{a+3}+\frac{1}{b+3}+\frac{1}{c+3}+\frac{1}{d+3}\le ...
4
votes
1answer
15 views

Solving Differential equations with Laplace transform

$\displaystyle y''+4y'+3y=e^{-t}$, given $\displaystyle y(0)=y'(0)=1$ My Attempt: Taking Laplace transforms on both sides $\displaystyle $ $\displaystyle [s^2\bar y-sy(0)-y'(0)]+4[s\bar ...
0
votes
1answer
22 views

Questions Number 8 and 9 from College Algebra CLEP Study Guide

Needing help with some more questions on my College Algebra Clep Study Guide. :/ I'm not looking for answers. I'm just looking to know how to solve some questions. Can anyone please help? ...
0
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2answers
20 views

Question Number 5 from College Algebra CLEP Study Guide

Needing help with some questions on my College Algebra Clep Study Guide. :/ I'm not looking for answers. I'm just looking to know how to solve some questions. Can anyone please help? ...
1
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3answers
23 views

Solving quadratic equations without the quadratic forumla

Is it possible to solve the following equation, in terms of $q$, without using the quadratic formula? $t - (m-q)^2 = v - (m-p)^2$ I asked a similar question this morning (about the quadratic ...
0
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0answers
25 views

Laplace transform - Heaviside algebra

I'm strugling with some algebra around a laplace transform with heaviside. The start function is $L(2tH(1-t)) + L(2H(t-1))$ so from this, I'm supposed to convert it to $L(2t) + L(2(1-t)H(t-1))$ ...
1
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1answer
25 views

rearrange $t - (m-q)^2 = v - (m-p)^2$ for quadratic formula form $ax^2 + bx +c = 0$ solving for $q$

I have the equation $t - (m-q)^2 = v - (m-p)^2$ which I would like to rearrange to be able to apply the quadratic formula, and solve in terms of $q$. Accordingly, it needs to be in the form: $ax^2 ...
0
votes
0answers
16 views

Rescaling of $|x_n - n|<1+\epsilon$ [on hold]

Good morning, I would like I would like to know a rescaling of $$|x_n - n|<1+\epsilon$$ with $0<\epsilon<1$, $x_n\in \mathbb R$, $n=0,\pm 1, \pm 2, \pm3, ...$ in this way: $$|x_m - ...
1
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3answers
37 views

solve $-(x_m - x_q)^2 = -(x_m - x_p)^2$ in terms of $x_q$

I have an equation, $-(x_m - x_q)^2 = -(x_m - x_p)^2$ which I want to solve in terms of $x_q$. I can see (by using a number line) that $q$ can have two solutions: $x_q = x_p$ or: $x_q = 2x_m-x_p$ ...
-1
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0answers
16 views

Calculate distance between two objects based on their visible height for a specific focal length

How do I calculate the distance between to objects of the same size base on their height for a given focal length. Both object 1 and object 2 are 15 cm in height (actual size). Object 2 looks ...
0
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4answers
57 views

Simplify $ (a^{-2} - b^{-2})/(a^{-1}-b^{-1})$ [on hold]

Simplify $$ (a^{-2} - b^{-2})/(a^{-1}-b^{-1}).$$ My answer is $\frac{1}{a+b}$. Am I correct? I had a precalculus final today and remembered this is a question.
2
votes
3answers
33 views

How do I find the domain of this function

I would like to know which operations i have to do to get the domain of this function: $$y=\sqrt{\frac{1}{x}-1}$$ I have researched and the solution of the inequality $\frac{1}{x}-1 \geq 0$ is ...
1
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3answers
35 views

Finding Horizontal/Oblique Asymptote of $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$

Is it correct to simply subsitute $\sqrt{x}$ with $x$ when finding horizontal or oblique asymptotes? The method works but I am not sure if it is formally sound enough to pass muster in an examination. ...
1
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2answers
27 views

“Full”-Simplification of arbitrary mathematical expressions

I've come across many (classroom) problems, like Roy did, whereby the solution to a problem, $$−3(7−2x)^2−5(1+x)^2$$ is the result of simplifying that expression as much as is possible, i.e. ...
0
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3answers
60 views

How to solve for $x$ for $\frac{1}2 x^{-1/2}- \frac14x^{-3/4}$

This is a derivative and I am trying to find the max and min. Right now I am trying to solve for x. $$\frac{1}2 x^{-1/2}- \frac14x^{-3/4}$$ $$\frac{1}{2 x^{1/2}}- \frac1{4x^{3/4}}$$ $$\frac{1}{2 ...
1
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3answers
29 views

How to find the general form (Ax-By-C = 0) of a line with an undefined slope

This is how the question reads: "The equation of the line that goes through the points (3, -6) and (3, 10) can be written in general form Ax + By + C = 0 where A = _ B = _ and C = ____" I know the ...
0
votes
2answers
18 views

Combining Functions Question

Question: If $f(x)=x^2-x+2$ and $g(x)=x-2$, find $h(x)$ such that $f(x)=g(h(x))$ I am not sure if I am on the right track here so far, I came to this mostly through guess and check, perhaps there is ...
0
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3answers
37 views

Factoring positive rational numbers

I don't understand how he goes from this: $$2n(a+b)+a-b=1\,\,\,; \forall n\in \mathbb{N^*}, \,\,\, \mathbb{N^*}=\{1,2,3,...\}$$, To this: $$\begin{cases} a+b=0 \\ a-b=1 \end{cases}$$
0
votes
4answers
67 views

Questions about solving inequality: $2 < \frac{3x+1}{2x+4}$

Solve the inequality: $2 < \frac{3x+1}{2x+4}$ Step 1: I simplified $\frac{3x+1}{2x+4}$ into: $3x+1-2x-4= x-3$. Step 2: $2>x-3$ Here I subtracted $2$ from both sides into: $x>-5$ or ...
0
votes
0answers
17 views

Can I evaluate polynomials with prime numbers to find possible irreductible factors?

Let $p(x,y)$, $c(x,y)$ and $d(x,y)$ be two variable polynomials with integer coefficients which satisfy $p(x,y)=c(x,y)\cdot d(x,y)$. Given $m, n$ positive prime numbers and given $e(x,y)$ another ...
1
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2answers
50 views

Inequality - Find what value of $t$ satisfies: $ (t/24) - (t+1) + (3t/8) < (5/12) (t+1)$

Inequality - Find what value of $t$ satisfies: $(t/24) - (t+1) + (3t/8) < (5/12) (t+1)$. Step 1: I multiplied both sides by $24$ and divided to get: $t-24(t+1)+9t < 10+24(t+1)$. Step 2: I ...
2
votes
4answers
59 views

Determined or not?

the function $\dfrac {2x}{3x-\sqrt{x} }$ is not derterined for values of $x$ equale or samller than zero, though when I take the limit $ \lim_{x \to 0^+} \dfrac {2x}{3x-\sqrt{x} }$ the output is zero ...
0
votes
3answers
109 views

Simplify tan$\theta$ cos$\theta$

How do I simplify tan$\theta$ cos$\theta$ ? Why is this so hard to do? What pieces of information should I know before doing these? Can someone just tell me were am I going wrong? I have 5 days ...
1
vote
2answers
86 views

limit of a rational function, $\lim _{x\to 1} \frac{x^3 +x-2}{1-x}$ [on hold]

$$\lim _{x\to 1} \frac{x^3 +x-2}{1-x}$$ can you please tell how to solve this ?! I tried too many things, non worked ! it is not zero for sure ! mathway gave me $-4$ (no steps)
1
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1answer
50 views

Finding cut-off point for utility function

OK, so apologies for the easy question, but I'm new to this! This is somewhere between elementary algebra, and beginner's game theory. The question comes from a paper I read here (see p. 193): ...
0
votes
3answers
50 views

Simplify $\tan(360 - \theta)$

I am aware that $\tan(\alpha-\beta)=\dfrac{\tan(\alpha)-\tan(\beta)}{1+\tan(\alpha)\tan(\beta)}$ So for my question: $\tan(360 - \theta)$ Do I choose random value for $\theta$ and plug it into the ...
1
vote
2answers
34 views

Number as sum of multiples of 3 and 5.

There were 10 questions on a test. A student gets 5 points for every correct answer and 3 points for every partially correct answer. If the student got 19 points, how many correct and partial ...
0
votes
3answers
55 views

Simplify $\sin (90 - \theta)$

Title. I have no idea what to do. Is their an identity I have to remember? What am I supposed to do to the equation? Do I have to solve for something first, what does it mean by simplify?
-2
votes
2answers
26 views

Solving Linear equation Gaussian method of elimination [on hold]

Solving linear equation Gaussian method of elimination $$\left\{ \eqalign{ -x-y & =7 \\ 4x-y & =-3 } ...
0
votes
1answer
28 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: ...
1
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4answers
1k views

What's wrong with my aproach to solving this equation with multiple logarithms?

A question I was faced with asked "For which $x$ is $\log_{10}(x)^{\log_{10}(\log_{10}(x))}= 10,000$?" My instincts tell me I can say $$\log_{10}(x)=10$$ and $$\log_{10}(\log_{10}(x))=4$$ However, ...
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votes
0answers
28 views

I got stuck with this question [on hold]

What is en equation of the circle in the standard $(x,y)$ coordinate plane that has a radius of 5 units and the same center as the circle determined by $x^2 + y^2 -6y+5=0$?
1
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0answers
21 views

Evaluation of a Hankel-like determinant

I consider the following determinant (Hankel-like?) $$ [f_1,f_2,...,f_n]:=\begin{vmatrix} f_1 & f_2 & \cdots & f_{n-1} & f_n\\ n-1 & f_1 & \cdots & f_{n-2}& f_{n-1}\\ 0 ...
1
vote
2answers
50 views

Graph a function

I have a question, I have a function: $$f(x) = \frac{-x^2-10x}{2}$$ I'm really confused how to replace the x. So, what would be the points in $y$ if $x$ were: $-4, -3, -2, -1, 0, 1, 2, 3, 4$?
0
votes
3answers
40 views

Trigonometric Identities help

How do you solve this? I can't figure out what I should do. $$\sin ^4\left(A\right)+\cos ^2\left(A\right)=\cos ^4\left(A\right)+\sin ^2\left(A\right)$$ Also, why is this equal zero? Can someone ...
1
vote
2answers
37 views

What are the solutions for $2 \sin^2 \theta − 1 = 0$?

Find all solutions of the given equation. I have $\pi/3 +2k\pi$ and $2\pi/3+2k\pi$. However, the computer program I am using says I am wrong.
0
votes
1answer
46 views

Check if point lies on a line segment

I know there are shorter solutions that use dot product, but I don't know what the logic behind doing so involves so I came up with something that I understand myself (i will research the dot product ...
0
votes
1answer
23 views

Find all solutions of the given equation √ 2 cos θ − 1 = 0 Let k be any integer. [on hold]

√ 2cos θ − 1 = 0 My answer is $(\pi/3+2k\pi)$ and $(5\pi/3+2k\pi)$ What am I doing wrong?
0
votes
2answers
45 views

Solve the given equation. sin^2 θ − 3 sin θ − 4 = 0

My answer is $\pi/2 + 2k \pi$ and $5\pi/2 + 2k \pi$. Webassign is marking me wrong however. Is it right?
0
votes
1answer
60 views

what is the coefficient of following expression

what is the co-efficient of $x^{50}$ in the expansion of $$\frac{1}{(1-x^{1.7})(1-x^{1.8})(1-x^{2.6})(1-x^{3.0})(1-x^{4.0})(1-x^{6.7})(1-x^{7.5})(1-x^{8.2})}$$ can you please explain me the logic
2
votes
2answers
101 views

Derivative of $(-2)^{x+1}$ [on hold]

Can we compute the derivative of $(-2)^{x+1}$? This may sound silly, but think about it. We cannot apply any of our formulae on it. I think we may have to go old school with this one
0
votes
3answers
41 views

Find all solutions of the given equation $\sec^2 θ − 4 = 0$. Let $k$ be any integer.

Find all solutions of the given equation: $$\sec^2 θ − 4 = 0$$ My answer is $\pi/4 + πk$ and $-pi/4 + πk$.
0
votes
2answers
56 views

How are $\pi/4$ and $3\pi/4$ solutions to $\sec^2 \theta -2 = 0$?

How are $\pi/4$ and $3\pi/4$ solutions to $\sec^2 \theta -2 = 0$ Please show work. I added two to both sides and then took the square root of each side to get $\sec\theta$ = $\sqrt2$ Where on the ...
0
votes
1answer
28 views

Double checking my progress on finding critical numbers

still cramming for the test tomorrow. (This cram has lasted most of my weekend) I'm having trouble with determining the critical values for this example problem. The problem is as follows: $$F(x) = ...
0
votes
1answer
29 views

Solve the given equation:$\cos\theta = -\sqrt{3}/2$ : List six specific solutions

Ok I understand that the initial equation is $\theta= 5\pi/6 + 2k\pi$ and $7\pi/6 + 2k\pi$ How do I calculate the other 4 values if $5\pi/6$ and $7\pi/6$ are my first 2.