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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8
votes
3answers
76 views

Intuition behind Descartes' Rule of Signs

I have read several places that Descartes' Rule of Signs was familiar to both Descartes and Newton, and that both considered it too "obvious" to merit a proof. I know how to prove it, but I would like ...
0
votes
1answer
13 views

If M = S, how to isolate a?

So I have to isolate $a$ in $M=S$ $M=1+\dfrac{a}{b}$ $S=a+b$ So, I put it up like this: $1+\dfrac{a}{b}=a+b$ ... right? But then what?
0
votes
1answer
22 views

what is the number of possibilities

I have 9 variables that can vary each from 0 to 100.(natural number). And the sum of the first 3 should be between 20 and 30. And the sum of the 9 variables should be equal to 100. What is the number ...
-1
votes
1answer
55 views

General Mathematics

Maths was never my subject. I can't answer this, could anyone help?. Is there some sort of formula that can be applied to scenarios like this? Thanks. A building firm employs 60 employees at a cost ...
0
votes
2answers
25 views

If $5^{(3x)} = 25^{(y+2)}$ and $x-2y=8$, then what is $x-y$?

The Question is If $5^{(3x)} = 25^{(y+2)}$ and $x-2y=8$, then what is $x-y$ ? The proposed answer: I do understand the first part that $3x=2y+4$ But the rest of the answer contains certain ...
0
votes
1answer
59 views

Fractions of Cracks

Sohrab is taking a long walk. He always finds it interesting to see how many sidewalk cracks he stepped on. The cracks are 5 1/4 feet apart. The cracks are very thin. His stride is 2 3/4 feet long ...
0
votes
2answers
46 views

What is a derivative of a function?

What does it mean by getting a derivative of a function?And how is it different from getting a limit? I know how to find the limit of a function but really do not understand what it is all ...
0
votes
0answers
9 views

Analytic solution to a maximization problem - Solve for $R$

I'm trying to use a CARA utility function $U(x)=e^{-\theta x}$ in the context of the Schumpeterian growth model to solve for the R&D spending. I set up a maximization problem \begin{equation} ...
1
vote
2answers
25 views

Precalculus converting radians to degrees.

I'm studying for a precalc test and I've kind of hit a brick wall with conversion. I've searched for help but only found things on converting from pi radians. I found some questions that consist of ...
1
vote
1answer
23 views

Volume of parallelpiped question?

I need to find the volume of a parallelpiped. The volume is spanned by 3 vectors $$\begin{cases}a=(-5,-3,2), \\ b=(1,0,2), \\ c=(2,-1,3), \end{cases}$$ so I tried with the formula $(a \times b) \cdot ...
0
votes
2answers
34 views

Solve the Following inequalities. $4/x < x$. Express answer in interval notation.

I am wondering how many intervals would I have to set up the chart. I keep on getting questions such as this wrong due to the fact that I don't evaluate the correct amount of intervals, My intervals ...
1
vote
1answer
41 views

In $1 < k < n-10^6$, what is $k$? (details in question)

This is a homework question of mine, I am not searching for the solution but rather what it means. It seems pretty straight forward but I am a little confused as to what the $k$ in $1 < k < ...
-4
votes
1answer
45 views

7=x√3 Solve this equation for X without using a calculator [closed]

7=x√3 solve for x DO NOT find the decimal answer of the √3 but keep it as a square root simplifying completely (this is from a 30, 60, 90 triangle)
0
votes
2answers
40 views

Is this a typo, or am I missing something?

I have a handout for my precalc II class. It says $\sinh(-x) = -\sin(x)$ It should be $\sinh(-x) = -\sinh(x)$ right? I don't see how a negative input could make a hyperbolic function circular.
1
vote
3answers
64 views

Solution of an equation, $x(\log\log9-\log\log x)=\log8$

How to find the solution of this equation analytically $x(\ln(\ln(9))−\ln(\ln(x)))=ln(8)$ Note:- I already know that the solution if this equality is 3, but I don't know how to find it analytical ( ...
0
votes
1answer
29 views

What are the steps done to solve this algebra question?

$$x^2 + 7x = 2$$ I came across a question similar to this one on my GED book, but instead of $= 2$ it was $= 0$. I changed the number to try and understand it better, but it just got much more ...
0
votes
3answers
21 views

Use the laws of Logarithms to express $\log_3(\sqrt{27}/9)$

Use the laws of Logarithms to express $\log_3\dfrac{\sqrt{27}}9$ My answer is $1/2$ Is there a certain game plan I should follow when solving logarithms. I can not use a calculator. Thanks in ...
1
vote
1answer
25 views

Making $-{{\pi i}\over n} e^{\alpha i}({{1 - e^{2 n \alpha i}\over{1-e^{2 \alpha i}}}})={\pi \over {n sin(\alpha)}}$; $\alpha={{2m+1}\over{2n}} \pi$

As part of a (much) longer problem in complex analysis, I need to show that the equality mentioned in the title makes sense, but I can't seem to find the right algebra tricks to get from point A to ...
0
votes
2answers
16 views

How do I set up a sign chart and graph for $\mathrm P(x) = \frac1{12}(x+2)^2(x-3)^2$.

How do I attack this problem $\mathrm P(x) = \frac1{12}(x+2)^2(x-3)^2$? Is $\frac1{12}$ consider a point on the chart? If so, do I add values to it? I know the zeros are $-2$ and $+3$ but what ...
0
votes
0answers
22 views

Is this basic proof complete?

I have a problem with proving that the limit as x goes to infinity for lnx/x is 0. Take the most basic approach: Note that the derivative of lnx is 1/x whereas x has a derivative of 1. Hence, lnx is ...
1
vote
2answers
37 views

What is this question about? Is it a standard form question????

I really dont understand these questions.. $x=9 \times 10^{2m}$ where $m$ is an integer. Find in standard form, an expression for $\sqrt{x}$ and... $y=9 \times 10^{2n}$ where $n$ is an integer Find ...
4
votes
2answers
337 views

How can I prove this trigonometric statement true?

$$ {1+\sin^{2}\left(x\right) \over \cos^{2}\left(x\right)} = 1 + 2\tan^{2}\left(x\right)$$ This statement is part of a larger problem, but I need to prove that this is true before moving on. I'm ...
4
votes
3answers
85 views

Is $|x-y|^n\leq 2^n(|x|^n+|y|^n)$?

Is $$|x-y|^n\leq 2^n(|x|^n+|y|^n)$$ for all $x,y\in\mathbb{R}$ and $n=1,2,3,\dots$ a standard inequality? If so, what's its name or how do you prove it?
1
vote
2answers
40 views

re-arrangement of a formula (regula falsi)

I am told $$ \frac{f(b)}{f(a)}=\frac{c-b}{c-a} \tag 1$$ which should give me $$ c= \frac{af(b)-bf(a)}{f(b)-f(a)} \tag 2$$ or alternatively $$ c= a + \frac{f(a)(a-b)}{f(b)-f(a)} \tag 3$$ But ...
1
vote
1answer
27 views

Distance, time and speed

Train $A$ leaves from station P to station Q, and at the same time train $B$ starts from station Q to station P on a parallel track. After meeting at point R, train $A$ takes $4$ hours and train $B$ ...
0
votes
1answer
27 views

Let f(x) = x+(2)/x. Rewrite f(x+h)-f(x)/h as a single reduced fraction

Let $f(x) = x+(2)/x$. Rewrite $(f(x+h)-f(x))/h$ as a single reduced fraction. My answer is $x^2 + xh - 2 / x (x+h)$ Am I right? Also, what is the best way to think of problem such as this? Should ...
0
votes
1answer
18 views

Solving $[(1-λ)a^{-p} +λb^{-p}]^{\frac{-1}{p}}=C$ for the variable $b$

How can I approach solving $[(1-λ)a^{-p} +λb^{-p}]^{\frac{-1}{p}}=C$ for the variable $b$ When the given answer is $$b =λ^{\frac{1}{pc^{p(1-λ)a^{-p^{\frac{-1}{p}}}}}}$$ Could someone elaborate the ...
-2
votes
2answers
35 views

Given $f(x)= 2x^2 -x+2$, find and simplify $\frac{f(x+h)-(x)}{h}$

My solution to this problem is $x^2+h-2/x(x=h)$ Am I right? Also, for a deeper understanding of this problem, one should always view the difference quotient as the input? Correct?
0
votes
1answer
14 views

Change base log formula?

Im trying to change the base log from ln to log with the following formula. y = a * ln⁡(x+c) + b The ln equation is: ...
1
vote
1answer
22 views

Solving $(1+ r/100)^t =2$ for the variable $r$

I have to solve the equation $(1+ r/100)^t =2$ for the variable $r$: I do have the end result $r=100(2^{1/2}-1)$, but the process it takes to reach this end result eludes me.
0
votes
2answers
27 views

normal distribution result with weird result

I was given this question in class: f(x) = -5x^2 + 30x -49 It looked like a fairly normal quadratic equation at first glance until i put it into the quadratic formula and got the values of x1 and x2 ...
2
votes
4answers
67 views

Contest problem involving primes and factorization

Prove that for any nonnegative integer $n$, the number $$5^{5^{n+1}}+ 5^{5^{n}}+1$$ is not prime. I want only some hints and the method to follow, but I don't need the full solution. Thanks.
4
votes
2answers
61 views

Is limits $\lim_{x\to\infty}{(x-2)^2\over2x+1}=\dfrac{1}{2}$?

$$\lim_{x\to\infty}{(x-2)^2\over2x+1}=\dfrac{1}{2}$$ I used an online calculator and it said it was actually $=\infty$ Here's how I calculate it: ...
1
vote
2answers
29 views

Sin & Cos Equation/Relation

If sin(x) = 0.3, find cos(pi-x) how i would solve this: let x = sin-1(0.3) solve for cos(pi-[sin-1(0.3)]) Is there a way to solve this by hand? Is the above method wrong?
0
votes
1answer
22 views

Exponential and Logarithmic Functions $\log_3 (x+7) - \log_3 (x-7) = 3$

Having trouble solving this problem. Where have I gone wrong? $$\log_3 (x+7) - \log_3 (x-7) = 3$$ $$\log_3 \left(\frac{x+7}{x-7}\right) = 3$$ $$\frac{x+7}{x-7} = 27$$ $$x+7 = 27 (x-7)$$ $$x + 7 = ...
-2
votes
1answer
28 views

planet x 1 hr equivalent for earth [closed]

I'm not a mathematician, so I need help, please show how to answer this question. If 1 day on earth = 1000 years in planet x then how many days will it be on earth if 1 hr passes on planet x? Update ...
1
vote
2answers
23 views

Exponential and Logarithmic Functions - $\log_2(x^2-4x-28)= 2$

I got $x= \frac{45}{x-4} $ I know its wrong. Can someone show me how to solve. Thanks
1
vote
1answer
41 views

Help with this trigonometry problem?

Is there an easier way of doing this problem: A square tower stands upon a horizontal plane. From a point in this place from which three of its upper corners are visible their angular elevations ...
0
votes
1answer
17 views

Pre calc question about cabon dating

Carbon dating. the radioactive element carbon-14 has a half-life of 5750 years. The percentage of Carbon-14 present in the remains of organic matter can be used to date the age of the organic matter. ...
0
votes
2answers
17 views

Modeling with Exponential and Logarithmic Functions

Been at this problem for an hour and I can't seem to solve it. Any takers? A certain culture of the bacterium Streptococcus A initially has 12 bacteria and is observed to double every 1.5 hours. ...
0
votes
0answers
27 views

Descartes' Rule of Signs

I have read several places that Descartes' Rule of Signs was familiar to both Descartes and Newton, and that both considered it too "obvious" to merit a proof. I know how to prove it, but I would like ...
0
votes
3answers
34 views

$\log_3 100 - \log_3 18 - \log_3 50$ [closed]

$$ \log_3{100} - \log_3{18} - \log_3{50} $$ How do I solve?
0
votes
1answer
21 views

Figures tangent to other figures

Find all values of $d$ where the graph of the polynomial $x^2-2014x+d$ is tangent to the graph of $x^2+2014x+y^2+2014y=-4056196$. $4056196=2014^2=(2*1007)^2=4(1007)^2$ $(x+1007)^2 ...
0
votes
3answers
26 views

How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.
2
votes
5answers
72 views

How do I find the y intercept for $P(x)= (x-1)^2(x-3)$?

I am sketching a graph of this polynomial $P(x)= (x-1)^2(x-3)$. I have the zeros, and I have made a sign diagram. Thus, I have all my values except for the $y$ intercept. How do I get it? If I ...
3
votes
2answers
73 views

Evaluating $\lim_{x\to1}\frac{x^2}{(x-1)^2}$

$\lim_{x\to1}\frac{x^2}{(x-1)^2}$ How do I calculate this limit? I can't use L'Hospital's rule here and dividing by $x^2$ doesn't work either. Thanks
0
votes
2answers
28 views

How can I prove that $2(\cos^6(x)-\sin^6(x))-3(\cos^4(x)+\sin^4(x))=-4\sin^6(x)-1$

How can I prove that $2(\cos^6(x)-\sin^6(x))-3(\cos^4(x)+\sin^4(x))=-4\sin^6(x)-1$ I tried to factor and I got $2\cos^4(x)+(-2\sin^2(x)-3)(\cos^4(x)+\sin^4(x))$ but that doesn't lead me to my goal. ...
0
votes
1answer
12 views

Polynomial Functions and Their Graphs - Seeking Help for a Deeper Understanding

Match the the polynomial function with one of the graphs I - IV. Give reasons for your choice. 1) P(x) = x(x^2-4) I chose number III because it reminded me of a power function raised to the 3rd ...
2
votes
3answers
213 views

Reason what 2^k in a sigma will do

I am trying to solve the following calculation without a calculator: $$\sum_{k=0}^82^k{8\choose k}$$ The first part: $$\sum_{k=0}^8{8\choose k}$$ is equal to $2^8$. I already know that the answer ...
2
votes
1answer
58 views

Sketch the Graph. $S(x) = \frac{1}{2} (x-1)^3 +4$

The question is: Sketch the graph of the the function by transforming the graph of an appropriate function of the form $y = x^n$. Indicate all x and y intercepts on the graph. I am really trying to ...