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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0
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2answers
177 views

If $ x = \log_{12} 27 \text {,then what is the the value of } \log_6 16 $?

How to proceed in this problem ?
0
votes
2answers
246 views

Simplification : $\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$

I am trying to simplify this expression by as usual the expansion way, $$\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$$ After some steps I am getting: $$4x^2 - y^2 - 2x^2y^2 - x^4y^2 = ...
0
votes
2answers
166 views

Solving $3 \cdot x^{\log_5 2} + 2^{\log_5 x} = 64$

I am facing some trouble in solving this equation: $$ 3\cdot x^{\log_5 2} + 2^{\log_5 x} = 64 $$ Give me some hints to proceed on this.
0
votes
1answer
505 views

Proving Logarithmic identity

Today, I read these two new Logarithmic identity $\displaystyle$ $$a^{\log_a m} = m $$ $$\log_{a^q}{m^p} = \frac{p}{q} \log_a m$$ Both of them seems new to me,so even after solving some problems ...
0
votes
7answers
850 views

Perpendicular bisector

"Show that BE is the perpendicular bisector to AC" I tried to prove this through Pythagoras, but the answer I got did not prove it was at a right angle, and therefore said it was not the ...
0
votes
0answers
223 views

tricky inequality [duplicate]

Possible Duplicate: problem with inequality How do I go about solving $0<1−\frac{an}{mb^2}e^{−r(T−t)}<1$, where a,b,T>t>0? I have been stuck here for some time now.
-1
votes
4answers
66 views

How can we find factorials in decimal form? [duplicate]

I've heard of factorials such as $5!$ and $3!$, which work like this: $5!=5\times4\times3\times2\times1=120$ and $3!=3\times2\times1=6$. At least this is what we get. Also, surprisingly, $0!=1$, but ...
-1
votes
3answers
72 views

Find the product of positive roots of equation $\sqrt{2008}\,x^{\log_{2008}x}=x^2$

Problem : Find the product of positive roots of equation $\sqrt{2008}\, x^{\log_{2008}x}=x^2$ Solution : The given equation can be written as $\sqrt{2008} \, x^{\log_{2008}x}=x^2 $ ...
-1
votes
4answers
95 views

using trial and error in math problems

Suppose one bacterium is in a jar at 12AM, and then suppose there are two bacteria at 12:30AM, and then there are four bacteria at 1AM, etc. (a) How many bacteria will be in the jar at 12PM that ...
-1
votes
3answers
302 views

Pre-Calculus Question: g(x) = $\sqrt[4]{x^2-6x}$ — Find the Domain

I can't for the life of me understand why the answer to this questions is $(-\infty,0] \cup [6,\infty)$ However, when I set the expression $x^2-6x \geq 0$, I get $x \geq 0$ and $x \geq 6$. Thus, I ...
-1
votes
2answers
43 views

Word Problems: Turning Sentences into Numbers

How do I go about solving the following problem? "A fourth of the product of a number and 8 is 3 times, and four less than, the number."
-1
votes
1answer
35 views

Linear transformation / Polynomial Question

$T:P_{3}\rightarrow P_{3}$ defined by $T(p(t))=tp'(t)+p(0)$ is a linear transformation. Determine whether $T$ is invertible. If yes, find $T^{-1}(q(t))$, where $q(t)$ is a polynomial of degree at ...
-1
votes
2answers
85 views

How To Evaluate This Limit and Find c?

For a certain value of $c$, $$ \lim_{x \to \infty}\left[\left(x^{5} + 7x^{4} + 2\right)^c - x\right] $$ is finite and non zero. Let $l$ be this limit. Calculate $l-2c$. The answer is $1$ but I am ...
-1
votes
2answers
187 views

A challenge on the parabola [closed]

Good Night ... Here I am editing the question and explaining the purpose of the same ... Mathematics course, and I love this science, I am very curious, and these days, studying a book of calculus ...
-1
votes
1answer
229 views

Word problem and formula algebra [closed]

$n(t)$ = $\dfrac{t^2}{2}-20t+k$ There was a 100 day period when the number of bees in a certain hive could be modeled by the function $n$ above.In the function , $k$ is a constant and $n(t)$ ...
-1
votes
3answers
150 views

An inequality with absolute value and a parameter: $|x-4|>a$

Solve : $|x-4|>a$. Case 1: $a>0$; Case 2: $a<0$ Progress I am getting answers which look similar in both cases: Let $a>0$ so $x>4+a$ or $x<4-a$ , Let $a<0$ so ...
-2
votes
0answers
15 views

Value of K that produces same remainder with two divisors? [closed]

$f(x)=3x^3+6x^2+Kx−4$I am having difficulty finding $K$ such that $f(x)$ has the same remainder when divided by $x-1$ and $x+2. Any help would be greatly appreciated.
-2
votes
1answer
37 views

Algebraic Word Problems [closed]

I have twice as many nickels as quarters. If all the coins are worth $4.90, how many quarters do I have? I know nickels are 5 cents and quarters are 25 cents, but how can I use this to figure out ...
-2
votes
2answers
94 views

How to solve the following equation by extracting square roots? [closed]

How to solve this equation by extracting square roots? $$9x^2=36$$ $$(x-12)^2=16$$ $$(x-5)^2=25$$ $$(x+2)^2=14$$ $$(4x+7)^2=44$$ $$(x+5)^2=(x+4)^2$$
-2
votes
1answer
190 views

if 30 out of 3500 drivers had an accident last year, what percent of the drivers had an accident

If 30 out of 3500 drivers had an accident last year, what percent of the drivers had an accident (round to the nearest tenth of percent)? plzz help me with this problem if you can and I will be ...
-2
votes
1answer
257 views

Finding $a_{2012}$

Assume $a_0=-2 , b_0=1$ which :$n\ge0$ and for each : $$a_{n+1}=a_n+b_n+\sqrt{a^2_n+b^2_n}$$ $$b_{n+1}=a_n+b_n-\sqrt{a^2_n+b^2_n}$$ How to find :$a_{2012}$
-3
votes
2answers
265 views

Polynomials: Quotient and Remainder [duplicate]

How can we find the quotient and remainder when: $$f(x)= x^5-x^4-4x^3+2x+3$$ is divided by $$g(x)=x-2?$$ Could someone please show how to step-by-step using synthetic division?
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votes
1answer
40 views

Who earn the most and who earn the least for this job?

Three brothers, A, B and C paint houses. They have been in the business so long that each knows exactly how many square feet he (and each of his brothers) paints in one hour and these rates never ...
-7
votes
0answers
49 views

how to factor this expressiion [on hold]

How to factor $\frac{2x^2-4x}{x+10}$ ?