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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
3
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Cost of a can (check my answer please)

Question goes...A can is in the shape of a circular cylinder is required to have a volume of 750 cubic centimeters. The top and bottom are made of material that costs 8 cents per square centimeter while the sides are made of a material that costs 5…
Ronnie.j
  • 331
3
votes
2 answers

$\log_{12} 2=m$ what's $\log_6 16$ in function of $m$?

Given $\log_{12} 2=m$ what's $\log_6 16$ in function of $m$? $\log_6 16 = \dfrac{\log_{12} 16}{\log_{12} 6}$ $\dfrac{\log_{12} 2^4}{\log_{12} 6}$ $\dfrac{4\log_{12} 2}{\log_{12} 6}$ $\dfrac{4\log_{12} 2}{\log_{12} 2+\log_{12}…
Kaeser
  • 331
3
votes
1 answer

Simplify the following indices

$3^{x+4} * 5^{x+7} * 15^{2x-1}$ I tried it in this way: $3^{x+4}*5^{x+1}*(3*5)^{2x-1}$ Then: $3^{x+4}*5^{x+1}*3^{2x-1}*5^{2x-1}$ And what about next?
Kiara
  • 900
3
votes
3 answers

Rationalize the denominator of the surd, giving your answer in the simplest form.

Rationalize the denominator of the surd, giving your answer in the simplest form. $\frac {3}{\sqrt2+5} $ Please help me... It must be like this right? $\frac {3}{\sqrt2+5} * \frac{\sqrt2-5}{\sqrt2-5}$
Kiara
  • 900
3
votes
1 answer

Binomial expansion with 2n power

I'm trying to expand $$(z+z^{-1})^{2n}$$. I've written the first 3 terms out but I can't figure out a way to work out the last 3 terms. I'm trying to produce an expression for $$\cos^{2n}x$$ using the complex numbers.
salman
  • 1,690
3
votes
1 answer

Simplify $\frac yx-\frac xy \over \frac 1y- \frac 1x$

$$\frac yx-\frac xy \over \frac 1y- \frac 1x$$ I am trying to solve this, I start with the top, multiply the left side by Y and the right side by x to get: $$\frac{y^2-x^2}{xy}$$ then I go to the bottom and multiply the left side by x and the right…
Joshhw
  • 603
3
votes
2 answers

GMAT work rate problem.

Person A makes 300 cakes in 2 hours. Person B makes 300 cakes in 2 hours. Person C makes 300 cakes in 3 hours How long does it take all 3 working together to make 300 cakes. (Assume no synergies and rates are additive. So Person A and Person B would…
Jwan622
  • 5,704
3
votes
1 answer

any help with how to do equations like this or what I can read is greatly appreciated

$$A_f=\frac{A_o}{1+\beta A_o}$$ rearranging for $\beta $ I get $A_f(1+\beta A_o)=A_o$ $A_f+A_f\beta A_o=A_o$ $A_f\beta A_o=A_o-A_f$ $$\beta = \frac{A_o-A_f}{A_oA_f}$$ The book shows, I don't see how they get…
bob a
  • 51
3
votes
2 answers

Find the value of A, B and C in the identities.

$6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(x - 1) + c$ Find the value of A, B and C. I started it like this: $6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(x - 1) + c$ Solving the right hand side: $ (ABx^2 - Ax - Bx + 1)(x - 1) + C$ $ ABx^3 - ABx^2 -…
Kiara
  • 900
3
votes
5 answers

How to get the man's age.

I am very much in need of solution for this problem. I can't figure out the answer for this. does anybody know about this problem below? thanks,, Problem: A man's boyhood lasted for 1/6 of his life, he played soccer for the next 1/12 of his life,…
user122935
  • 51
3
votes
1 answer

Negative Radicals

I do not understand this question at all! Could someone please help out a person who is horrible at math? I'm desperate! $\sqrt{−x^2}$ is defined only for $x = 0$, but $\sqrt{−x}$ is defined for all non‐positive real numbers. Explain why these…
UVic Student
  • 77
3
votes
3 answers

Solve $ax^t = by^t$ for $ t$

I use to know how to do this but a friend of mine asked for help and I cannot remember. Can anyone help me solve $ax^t = by^t$ for $t$?
biw
  • 211
3
votes
0 answers

Roots of a polynomial. Rotating the unknown quantity

Let $r\in\mathbb{R}$, $p\in\mathbb{C}\left[ x\right] $ and $q\left( x\right) =p\left( ix\right) $. The following reasoning is false: $p\left( r\right) =0$ iff $p\left( i\left( -ir\right) \right) =0$ iff $q\left( -ir\right) =0$; but…
Juan Ignacio
  • 71
3
votes
3 answers

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be multiplicative. Is it exponential?

For function $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfies $f\left(x+y\right)=f\left(x\right)f\left(y\right)$ and is not the zero-function I can prove that $f\left(1\right)>0$ and $f\left(x\right)=f\left(1\right)^{x}$ for each…
drhab
  • 151,093
3
votes
1 answer

partial fraction expansion

So this is a solution to this partial fraction. I understand everything except the final line. I know how the first term 4x0.5/.... came about. I do NOT know how the second and third term 1/s - (....) came about from the previous line's second…
user122415
  • 361
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