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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
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Hard algebra problem

Given $$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ Now, it is necessary to find $$\frac{x^2}{a^4}+\frac{y^2}{b^4}+\frac{z^2}{c^4}=?$$ Is this possible and how? a,b,c are given constants. I think, ? is probably a complicated…
Martin Gales
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How to determine $x$ and $y$ intercepts for $y = 4(x - 2)^2(x + 2)^3$

I need help to determine $x$ and $y$ intercepts for $$ y = 4(x - 2)^2(x + 2)^3 $$ I guess my first question is, do I need to get the equation into $$ ax^3 + bx^2 + cx + d $$ form before starting?
erimar77
  • 741
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To solve $2^x+4^x+2^{\lfloor x \rfloor}+4^{\lfloor x \rfloor}+2^{x- \lfloor x \rfloor}-4^{x-\lfloor x \rfloor}=50+\sqrt{50}$

How to solve for positive real $x$: $$2^x+4^x+2^{\lfloor x \rfloor}+4^{\lfloor x \rfloor}+2^{x- \lfloor x \rfloor}-4^{x-\lfloor x \rfloor}=50+\sqrt{50}$$ ?
user123733
3
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1 answer

Finding a real root in a cubic equation?

I am trying to find a real root of the following cubic. $x^3-6x^2+14x-15=0$ I did $x=y-\frac{b}{3a}$ which is $x=y+2$ I plugged my substitution to get the depressing cubic. $(y+2)^3-6(y+2)^2+14(y+2)-15=0$ which is $y^3+2y=3$ then I set up the…
Fernando Martinez
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Solving cubic equation?

I am trying to figure out the following cubic root thing. $ax^3+bx^2+cx+d=0$ I set up $x=y-\frac{3}{ba}$ Then I plug in for x $a(y-\frac{3}{ba})^3+b(y-\frac{3}{3a})^2+c(y-\frac{3}{ba})=0$ The issue I am having trouble with is the simplification I…
Fernando Martinez
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3
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1 answer

Statistics - Average

I'm working on an 8th grade math book and came across this problem: In a class, the average marks of the boys and girls are 520 and 420 respectively. And the average marks per student is 500. What is the percentage of boys in the class? This seemed…
Ramana
  • 471
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2 answers

no. of Digit in $x^y\;,$ where $x,y\in \mathbb{N}$

$(1)$:: Calculation of no. of Digits in $2^{100}$ .$(2)$:: Calculation of no. of Digits in $3^{100}$. If it is given that $\log_{10}(2)=0.3010$ and $\log_{10}(3) = 0.4771$ $\bf{My\; Try::}$ I have seen in book and it is given as :: $(1)$ no. of…
juantheron
  • 53,015
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no. of straight line, and triangle by joining points in a plane

Out of $18$ points in a plane, no three are in same straight line except $5$ points which are collinear. Then the number of $(a)$ Straight lines $(b)$ Triangles which can be formed by joining them. $\bf{My\; Solution::}$ $(a)$ For calculation of…
juantheron
  • 53,015
3
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1 answer

Help setting up an equation expressing perimeter as a function of $x$

A line is drawn from the origin $O$ to a point $P(x,y)$ in the first quadrant on the graph of $y=\frac{1}{x}$. From point $P$, a line is drawn perpendicular to the $x$-axis, meeting the $x$-axis at $B$. Express the perimeter of $OPB$ as a function…
erimar77
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1 answer

Rewritting a messy cubic root

Is there a really quick way of showing that: $$\sqrt[3]{49-25\sqrt{2}}$$ Can be written in the form: $$a+b\sqrt{2}$$ Is there a way to generalize which integers $a$ and $b$ can be rewritten in such a way?
Jackson
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By considering bounds, work out V to a suitable degree of accuracy

I keep getting this question in my GCSE papers, but I have no idea how to solve it, and everywhere I look there doesn't seem to be a simple answer. The general question goes like this: $$v=\sqrt{\frac{a}{b}}$$ $a = 6.43$ correct to 2 decimal…
Derek
  • 131
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1 answer

Volume and lateral surface area are equal

I need to express the radius $r$ of the right circular cone as a function of its height $h$ given that its volume equals to its lateral surface area. I know the two equations $\pi r \times \sqrt{r^2 + h^2}$ and the volume $\frac{\pi}{3} r^2 h$. …
erimar77
  • 741
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1 answer

Find $(\delta-\alpha)(\gamma-\alpha)(\delta-\beta)(\gamma-\beta)$ as a polynomial of p,q,r,s

The equation $x^2+px+q=0$ has roots $\alpha , \beta$; the equation $y^2+ry+s=0$has roots $\delta, \gamma$. Find $$(\delta-\alpha)(\gamma-\alpha)(\delta-\beta)(\gamma-\beta)$$ as a polynomial of p,q,r,s.( This polynomial is called the resultant of…
mikoyan
  • 1,135
3
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1 answer

Expanding $(2y-2)^2$ by FOIL

Expanding $(2y-2)^2$ Isn't this same as \begin{gather*} (2y-2)(2y-2)\\ = 4y^2-6y+4\ ? \end{gather*} This should be FOIL, shouldn't it?
Liger86
  • 427
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1 answer

Maximum area limited by circumference

The circumference is equal to 10, I am to find x and y (as drawn on the picture) so that the area is as great as possible. I have tried back and forth here. $A = \frac{\pi y^2}{8} +xy$ $10 = \frac{y\pi}{2} + 2y + 2x $ When finding a maximum I…
Algific
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