Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

47234 questions
6
votes
2 answers

simplification of trig identities math check

I'm looking over some class notes, and I'm sure that my professor has made an error. Consider the following equation: $$ e^{-q} \sin \left(kx - \omega{t} \right) - e^{q} \sin \left(kx + \omega{t} \right)$$ In my notes, this can be simplified as: $$…
Emma Tebbs
  • 215
6
votes
3 answers

How did Sir Isaac Newton develop and formulate the famous binomial theorem?

After completing combination, I have started to read Binomial Theorem. My book only mentioned about Pascal's Triangle. And the formula was then given straightforward. But how did Sir Issac Newton actually develop this theorem?? How did he formulate…
user142971
6
votes
1 answer

Max. and Min. value of $f(\phi) = \frac{1+\cos \phi}{2+\sin \phi}.$

Calculation of Max. and Min. value of $\displaystyle f(\phi) = \frac{1+\cos \phi}{2+\sin \phi}.$ $\bf{My\; Solution::}$ Let $\displaystyle y = \frac{1+\cos \phi}{2+\sin \phi}\Rightarrow 2y+y\sin \phi = 1+\cos \phi$ So $y\cdot \sin \phi - 1\cdot…
juantheron
  • 53,015
5
votes
3 answers

finding the positive integre solutions $x^2+5xy=5775$

Given the equation: $x^2+5xy=5775$. How can i find the positive integer solutions of it? I can write it as $x(x+5y)=5775$ but it seems to be hard to guess. Thanks.
david
  • 53
5
votes
2 answers

Finding a function with certain properties

I ran into a problem, and I'm not sure how to continue. Problem: Let $f$ be a function such that $\sqrt {x - \sqrt { x + f(x) } } = f(x)$, for $x > 1$. In that domain, $f(x)$ has the form $\dfrac{a+\sqrt{cx+d}}{b}$, where $a$, $b$, $c$, $d$ are…
Pakquebchsoflwty
  • 696
5
votes
1 answer

Efficiently solving algebraic equation

I would like to solve following equation: $$15 (x+2)^{-4} = 11(x+2)^{-2} +4$$ I would first remove the negative power by adding $(x+2)^4$ Then I get $$15 = 11(x+2)^2 + 4(x+2)^4\\ 11(x+2)^2 + 4(x+2)^4 -15 = 0$$ should I do now a quadratic equation…
user164612
5
votes
2 answers

Sum of roots of an equation $\sqrt{x-1}+\sqrt{2x-1}=x$

Find the sum of the roots of the equation $\sqrt{x-1}+\sqrt{2x-1}=x$ My attempt: Squaring the equation: $(x-1)+(2x-1) +2\sqrt{(x-1)(2x-1)}=x^2$ $\implies x^2-3x+2=2\sqrt{(x-1)(2x-1)} $ $\implies (x-1)(x-2)=2\sqrt{(x-1)(2x-1)} $ $\implies…
square_one
  • 2,317
5
votes
1 answer

I get two different answers on simple equation. What am I doing wrong?

For the equation: $-x^2 = -2x(3x+1)$ I can either multiply it out on the right side and get a $-6x^2-2x$ or just divide both sides by $-2x$. However, when divide out both sides, I just get one answer: $-2/5$. When I multiply it out, I get two…
Joe
  • 141
  • 9
5
votes
4 answers

Why is slope rise/run?

What makes slope rise over run? What makes the standard equation for a line use a slope of rise over run as opposed to run over rise? What would the standard equation of a line look like if m was equal to run/rise $\frac{\Delta x}{\Delta y}$
user16795
  • 169
5
votes
2 answers

How to solve $-20=15 \sin \theta- 30.98 \cos \theta$?

How can I solve the following equation? $$-20=15 \sin \theta- 30.98 \cos \theta$$ I can't think of any way to solve it. You can't factor out cosine because of the annoying little negative twenty, and if you divide by cosine you also get nowhere.
Jason
  • 3,563
5
votes
1 answer

Solve $\sqrt x = x/2$.

If $f(x) = \sqrt x$ and $g(x) = x/2$, find the area of this limited area between $f(x)$ and $g(x)$. I am having trouble solving this equation $\sqrt x = x/2$ that should give me the x values. I know that the next step after this one is to solve…
S4M1R
  • 701
5
votes
4 answers

Tricky Factorization

How do I factor this expression: $$ 0.09e^{2t} + 0.24e^{-t} + 0.34 + 0.24e^t + 0.09e^{-2t} ? $$ By trial and error I got $$ \left(0.3e^t + 0.4 + 0.3 e^{-t}\right)^2$$ but I'd like to know how to formally arrive at it. Thanks.
jojo
  • 163
5
votes
3 answers

Determining whether points are collinear

$(1,1)(3,9)(6,21)$ The way I figured that this should be solved is by finding the slope of: $(1,1)(3,9)$ Then, $(3,9)(6,21)$ Finally $(1,1)(6,21)$ Which are 4, 4,and 4 respectively. So I assume that they are collinear. Am I correct? And if not,…
Cherry_Developer
  • 4,239
5
votes
2 answers

Slope of a vertical line

Find the equation of the line that satisfies the given conditions: Through $(-1,2)$; parallel to the line $x=5$ I know that the equation of this line is $x=-1$ because $x=5$ is a vertical line and any line parallel to it would be vertical as well.…
Cherry_Developer
  • 4,239
5
votes
2 answers

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 others.
Cherry_Developer
  • 4,239
1 2 3
…
99 100