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.

learn more… | top users | synonyms (2)

2
votes
2answers
854 views

Take set of values and change scale [duplicate]

I have a large array of variable-integer keypairs. The integer values range from -5 to 5. I'd like to scale that data to a range of 0 to 2. Logically, -5 would become 0, 0 would become 1 and 5 would ...
0
votes
2answers
83 views

Maximum value of the function

Find the minimum value of $f(x) = \max\{x^2-4, x , - 1\}$ I am able to do this question by using graph. But if there is any other method please tell me
3
votes
4answers
218 views

the solution set of $\left | \frac{2x - 3}{2x + 3} \right |< 1$

what is the solution set of $\left | \frac{2x - 3}{2x + 3} \right |< 1$ ? I solved it by first assuming: $-1 < \frac{2x - 3}{2x + 3 } < 1$ ended with: $x > 0 > -3/2$ Is that a ...
6
votes
7answers
333 views

What is the result of sum $\sum\limits_{i=0}^n 2^i$ [duplicate]

Possible Duplicate: the sum of powers of $2$ between $2^0$ and $2^n$ What is the result of $$2^0 + 2^1 + 2^2 + \cdots + 2^{n-1} + 2^n\ ?$$ Is there a formula on this? and how to prove the ...
2
votes
1answer
305 views

Intersection between two functions?

How do I find the intersection between $f(x) = 3(x-2)^2$ and $g(x) = 3\sin(x-4)$? It's a sinusodial function so it I couldn't solve it like a normal intersection.
8
votes
6answers
591 views

Is it wrong to say $ \sqrt{x} \times \sqrt{x} =\pm x,\forall x \in \mathbb{R}$?

Is it wrong to say $$ \sqrt{x} \times \sqrt{x} =\sqrt{x^2}= \pm x$$ I am quite sure that $\sqrt{(x)^2} = \pm(x)$ But, does $\sqrt{x } \times \sqrt{x} =- (x)$ doesn't holds in $\mathbb{R}$ but if we ...
1
vote
1answer
662 views

Using Parametric Equations to Define the Position of an Object in Motion

What is the intuition behind the equations for the parametric equation applications below? Rather than memorize the formulas for a quiz i'd like to gain a deep understanding of them.
1
vote
2answers
308 views

What is the underlying function?

I have some value pairs. They are inversely proportional. I want to have a formula to get the second value from the first value. ...
3
votes
5answers
75 views

Analyzing a mixture issue.

I am having a problem with this question: Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ ...
5
votes
4answers
189 views

How do I solve this problem?

Exercise: If $a+2b=125$ and $b+c=348$, find out $2a+7b+3c$. Here $a$, $b$, $c$ are natural numbers. The answer is: $2a+7b+3c = 1294$ I tried but just can't figure out how to get to this answer. ...
1
vote
2answers
77 views

A question about similar triangles.

Please, I would like help in solving this problem: The sides of a triangle measure 2,3 and 4 cm respectively. The perimeter of a similar triangle is 36 cm. I want to find the length of each side of ...
1
vote
1answer
99 views

Why is the following % profit answer wrong

The question is: A merchant buys an old carpet for $25 dollars.He spends 15 dollars to have it returned to to good condition and then sells it for 50 dollars . What is percent profit of his total ...
17
votes
2answers
353 views

Rigorous proof that $\displaystyle\frac{1}{3} = 0.333\ldots$

I'm a PreCalculus student trying to find a rigorous proof that $\displaystyle\frac{1}{3} = 0.333\ldots$, but I couldn't find it. I think (just think) that this proof would start by proving that ...
2
votes
3answers
38 views

Combining a radical and simplifying?

How would I combine and simplify the following radical: $$\sqrt {\frac{A^2}{2}} - \sqrt \frac{A^2}{8}$$
1
vote
2answers
97 views

Simplifying a radical?

How would I simplify the following two radicals. $$\sqrt{\frac{X^3}{50}}$$ For my answer I got $\frac{X^2}{50X}$ but I am not sure if this is correct. My second question is how would I simplify ...
1
vote
2answers
68 views

Radical question simplify?

How would you simplify the following radical. $$\sqrt\frac1B$$ I am kind of confused do I multiply the numerator and denominator by B.
9
votes
3answers
781 views

How do I “learn” more difficult algebra?

I do not really understand where I was suppose to learn this kind of stuff. I am always told that my algebra knowledge is the biggest reason I am so bad at math. But I do not understand where I was ...
8
votes
2answers
325 views

Question Regarding Cardano's Formula

In Cardano's derivation of a root of the cubic polynomial $f(X)=X^3+bX+c$ he splits the variable $X$ into two variables $u$ and $v$ together with the relationship that $u+v=X$. From this he finds that ...
1
vote
1answer
170 views

Should students be taught that $\int dx/x = \log(|x|)$? [closed]

I think in precalculus students should be taught the following: Euler's identity for $e^{i \theta}$. The principal value of $log(x)$ for $x<0$. Then in Calculus they should be taught that $\int ...
1
vote
1answer
101 views

Parametric equation involving exponents and e

How do you go about solving this problem? For each plane curve given below, find a rectangular equation. State the appropritate interval for $x$ and $y$. $x(t) = e^{5t}$, $y(t) = e^t$, $t \in ...
0
votes
1answer
266 views

convert rotation in degrees to percent to move an object x and y directions

So I have been out of school for a very long time and have a forehead slapping question: $$ m = \tan(\theta) $$ where $ \theta $ is an angle, but all that gives me is $ \frac yx $. I need to know ...
35
votes
25answers
6k views

“Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
0
votes
1answer
43 views

Solving an equation with precondition

How do I solve the following equation: $$x + y\ne0\text{ and }\frac{1}{x+y}=x$$ Wolfram Alpha came up with this solution $$x\ne0,\:y=\frac{1-x^2}{x}$$ but I don't know how to get there. thx alex
1
vote
2answers
653 views

Find a number such that the sum of the number and its square will be as small as possible.

Find a number such that the sum of the number and its square will be as small as possible. Please try to explain as well as you can.
0
votes
1answer
229 views

Given $x^2 + 2y^2 - 6x + 4y + 7 = 0$, find center, foci, vertex/vertices

So the equation is: $$ x^2 + 2y^2 - 6x + 4y + 7 = 0 $$ Find the coordinates of the center, the foci, and the vertex or vertices. What I did was put the equation in the form: $$ ...
3
votes
4answers
485 views

Spivak Calculus Prologue

I'm completely blown away by the difficulty of Spivak. I've managed to work through the first 3 problems, but I feel I'm missing something important to solve these basic inequalities in his 4th ...
3
votes
2answers
713 views

Intersection of two lines using general form

How do I find the intersection of these two lines with their equations in general form. I don't want to graph them and I'm wondering if its possible with out converting them to gradient intercept ...
2
votes
2answers
70 views

Solving a quadratic?

Lets say you have a quadratic that you factor into root form. To solve for the roots, you let the $y$ value be $0$: $0 = (x_1-h)(x_2-k)$ Following this you would divide both sides by one of the ...
1
vote
3answers
134 views

Solving a biquadratic $x^{4}-2x^3 + x^2 - 2x +1 =0$

How do I find the roots of $$x^{4}-2x^3 + x^2 - 2x +1 =0$$ I am not able to find any roots by trial and error.
1
vote
2answers
92 views

Theorem about two real numbers 2

My question is: Prove- If $a,b$ are two positive real numbers such that their sum is $a+b=k$. Then the product $ab$ is maximum if and only if $a=b=\displaystyle\frac{k}{2}$. I proved the ...
1
vote
3answers
110 views

Simplify these expressions with radical sign 2

My question is 1) Rationalize the denominator: $$\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$$ My answer is: $$\frac{\sqrt{12}+\sqrt{18}-\sqrt{30}}{18}$$ My question is 2) ...
1
vote
2answers
57 views

Reducing a fraction in algebra?

How would I reduce the following fraction? $$\frac{4A^2-B^2}{4A^2-4AB+B^2}$$ I am not sure how I would reduce it.
4
votes
1answer
167 views

Good in-depth books for precalc?

I'm trying to brush up on algebra and precalc to remember stuff I used to know and learn stuff I didn't get to. Trying to pass the accuplacer placement test and test into calculus, so im trying to ...
0
votes
1answer
111 views

Simplify this expression with radical signs

My question is- Simplify: $$\frac{1}{\sqrt{3}+\sqrt{2}} + \frac{2}{\sqrt{5}-\sqrt{3}} - \frac{3}{\sqrt{2}+\sqrt{5}}$$ My answer is $2\sqrt{3}$. Am I right? I would also like to know the solution as ...
1
vote
5answers
671 views

Simplify this expression with nested radical signs

My question is- Simplify: $$\frac1{\sqrt{12-2\sqrt{35}}}-\frac2{\sqrt{10+2\sqrt{21}}}-\frac1{\sqrt{8+2\sqrt{15}}}$$
3
votes
1answer
392 views

Solve the general cubic by factoring

After learning Cardano's solution of the cubic, I decided to look at Ferrari's solution of the quartic (both articles on Wikipedia). At the end of the article on the quartic function was an an ...
1
vote
3answers
91 views

How to calculate these summations?

How to find the values of these kind of summations: $$\large\sum_{i=0}^6(6-i)\;\ast\;\sum_{j=1}^6(7-j)\;\ast\;\sum_{k=2}^7(8-k)\;\ast\;\sum_{\ell=3}^8(9-\ell)$$
5
votes
2answers
1k views

Is $r=2\cos(\theta)$ a one-petal polar function?

I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
7
votes
4answers
203 views

Theorem about two real numbers

My question is: $a,b$ are two positive real numbers such that their product is constant,equal to $k$ say. Prove: the sum $a+b$ is minimum if and only if $a = b= \sqrt k$. Can this be solved using ...
0
votes
1answer
136 views

Undefined natural logarithm?

The natural logarithm is the logarithm to the base $e$, where $e$ is an irrational and transcendental constant. $$e=\lim_{n\to \infty}\left(1+\frac {1}{n}\right)^n.$$ $$\ln a=\log_{e} a.$$ I know ...
2
votes
2answers
93 views

Reducing a fraction?

How would I reduce this fraction? $$\frac{km+kn}{n^2+nm}$$ I think it would be $\frac{2k}{n^2}$ but I am not sure.
2
votes
4answers
306 views

How to solve this quartic equation?

For the quartic equation: $$x^4 - x^3 + 4x^2 + 3x + 5 = 0$$ I tried Ferrari so far and a few others but I just can't get its complex solutions. I know it has no real solutions.
8
votes
3answers
549 views

If two parabolas don't intersect, is there a line that doesn't intersect either of them?

Two parabolas in a plane are given, such that they don't intersect. Is it true that there is a line in plane such that doesn't intersect any of them?
-3
votes
3answers
893 views

Simplifying $\sqrt {1+(x/2 - 1/(2x))^2}$

I am having trouble figuring this out. $$\sqrt {1+\left(\frac{x}{2}- \frac{1}{2x}\right)^2}$$ I know that $$\left(\frac{x}{2} - \frac{1}{2x}\right)^2=\frac{x^2}{4} - \frac{1}{2} + \frac{1}{4x^2}$$ ...
1
vote
1answer
80 views

Does this inequality hold in general?

If I have functions $f,g,h > 0$ and $f\le g+h$ then: $$\frac f{f+1}\le \frac g{g+1}+\frac h{h+1}, x \in R$$ I have been trying to find out whether it's true or not but I haven't succeeded.
4
votes
2answers
319 views

How can we solve: $\sqrt{x} - \ln(x) -1 = 0$?

How could we solve $$\sqrt{x} - \ln(x) -1 = 0$$ without using Mathematica? Obviously a solution is $x = 1$, but what are the other exact solutions? This question is inspired by my first question How ...
3
votes
2answers
544 views

How can we solve: $\sqrt{x} + \ln(x) -1 = 0$?

How could we solve $$\sqrt{x} + \ln(x) -1 = 0$$ without using Mathematica? Obviously a solution is $x = 1$, but what are the other exact solutions?
2
votes
3answers
1k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
2
votes
5answers
312 views

$3x^3 = 24$ quadratic equation

Completing the square I know by factoring $$x^3 - 8 = 0\\ x-2 = 0$$ that one of the solutions is 2. but the other solutions is $1 ± i \sqrt 3$. Can someone explain to me how to get that?
4
votes
1answer
161 views

quadratic inequality

I do a procedure for solving algebraic inequalities of the second ($x^2+bx+c>0$) degree for my student. I know it is possible to solve the inequality by factorisation, Solving a quadratic ...