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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1
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2answers
27 views

Find the sum of an infinite series of Fibonacci numbers divided by doubling numbers.

How would I find the sum of an infinite number of fractions, where there are Fibonacci numbers as the numerators (increasing by one term each time) and numbers (starting at one) which double each ...
2
votes
2answers
34 views

Is there a way to get the closed form of $x$ considering $x^2 + 3x = \sqrt{x + 2}$, not using calculator/computer?

How would one go about finding the exact answer to $$x^2 + 3x = \sqrt{x + 2}$$ Solving for $x$? Using paper and pencil to plot a graph, I've found the solution lies at $\approx 0.453$, but I am ...
-4
votes
3answers
48 views

Solving $x^2-6=\sqrt{x+6}$ [on hold]

How can I solve: $$ x^2-6=\sqrt{x+6}$$ Thanks for any help.
0
votes
0answers
35 views

Solving equations, Math olympiad, using vieta relation?

So the question asks to solve for real valued $a$ such that $b,c,d\in\mathbb{R}$ $$abcd=-1$$ $$(a+b)(c+d)=-1$$ $$ac+bd+a+b+c+d=-1$$ $$ab+cd=ac+a+c$$ So assuming the four numbers are roots of a quartic ...
1
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2answers
20 views

Find one set of solutions for the following system:

Find one set of solutions for the following system: \begin{cases} 1+a^2+d^2=3+b^2+e^2=3+c^2+f^2 \\ 1+ab+de=0 \\ ac+df=0 \\ bc+ef=0 \\ \end{cases}
2
votes
2answers
32 views

Probability of 8 or 9 digit sequence colliding in the same place in two 65 digit numbers

I have two numbers: 3032643431333337636238613038343231383364303731376566303037663231 3861663464383131656131653461343961343364303737663565356561653361 36430373 ...
7
votes
1answer
43 views

How do I find a constant for a polynomial so its roots are reflective around a linear function?

How can I find all complex numbers $w$ so that the roots of the following polynomial are reflected around a linear function $f(x)$ $$p(q) = q^2-4q+w = 0$$ If I want to find all the complex numbers ...
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0answers
23 views

Explain why every natural number (other than one) is divisible by at least one prime number? [on hold]

Explain why every natural number (other than one) is divisible by at least one prime number? This is through Euclid's idea. A prime number is a natural number with exactly two distinct positive ...
3
votes
3answers
106 views

Solve $\frac{x^2+2xy+y^2}{x^2-y^2} >x+y$

Find the set of integer solutions $(x,y)$ to $$\frac{x^2+2xy+y^2}{x^2-y^2} >x+y$$ I can't seem to multiply both sides by the expression in the denominator. Nor can I simplify and cancel any ...
-1
votes
1answer
13 views

Trapezoids and Bases [on hold]

A trapezoid has bases of length $x$ and $4$. Let $P$ and $H$ be points on opposite legs of the trapezoid. $PH$ is parallel to the bases and divides the trapezoid into two quadrilaterals of the same ...
0
votes
2answers
22 views

Finding relationship between two numbers directly that were changed cumulatively

Bear with me. I'm not sure how to express this question let alone answer it. Here goes... I have a program that can calculate change from a single rate, we'll call 'A'. Known: $$C = A + 400$$ ...
1
vote
1answer
18 views

Third degree polynomial with unknown coefficients $q^3-3aq^2+b^2q+c = 0$

For an equation $q^3-3aq^2+b^2q+c = 0$ we know the roots $c, (a+b), (a-b)$. What is a good place to start with such equations? I've tried setting up a system of equations, but this is supposed to be ...
-1
votes
1answer
53 views

Mathematically prove that a bench which 2 chidlren fit in can't fit 3. [on hold]

You have a bench( Only 2 children can sit on it), 3 children and you have to prove logically that 3 children don't fit on the bench.
1
vote
2answers
23 views

How do I solve for $\delta$ in this question

$316.45 = 100e^{\delta(10)} + 100e^{\delta(5)}$ I don't know why I can't do this. I thought of using $\ln$ but I don't think $\ln(A+B) = \ln(A) + \ln(B)$ or does it?
0
votes
4answers
79 views

How do I solve this one? It's irritating me!

How do I solve this question? I can't think of anything to do! As $(x,y)$ ranges over all pairs of real values, what is the smallest value of: $(2x-3y-4)^{ 2 }+(2x-3y+10)^{ 2 }$
0
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2answers
32 views

Expand $-(x-2y)^2$

I'm having a hard time solving this. this is a part of a bigger "count sequence" and I need to expand: $$-(x-2y)^2$$ Bigger "part": $$(x+2y)^2-(x-2y)^2-4x(2y-1)$$ Doesn't matter how much I twist ...
0
votes
0answers
23 views

Silly technical question about polynomials in Lagrange's “résolution algébrique”

I decided that I'd go through Lagrange's "Sur la Résolution Algébrique des Équations" (see, if you have the time, a previous, unanswered question of mine: Value in retracing mathematicians' steps ...
2
votes
0answers
25 views

Interchanging Powers

Let $f(x)=(x^b)^{1/a}$ and $g(x)=(x^{1/a})^b$, where $a,b$ are even numbers. The domains are clearly different. $\operatorname{dom}\{ f\}=\mathbb{R}$, while $\operatorname{dom}\{ g\}=\mathbb{R}^+_0$. ...
1
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1answer
21 views

Calculating Covariance missing understanding for one step

I am following this once I get to this point I don't understand the transition/calculation to get -0.01 I mean to me that equals ...
0
votes
1answer
19 views

How do I get an Archimedean spiral that decreases from an initial radius?

So, where the equation of an archimedean spiral is: $$r = a + b\theta$$ I want to be able to use the equation in this form to then have a function where r decreases in exactly the same way by an ...
2
votes
4answers
65 views

Solving $y^2 - yx - y + x = 0$ for $y$?

I solved this equation for $y$ by inspection and confirmed it with Wolfram Alpha - $y^2 - yx - y + x = 0$ I got the values $y = 1$ and $y = x$ However I was wondering is there a formal method for ...
0
votes
1answer
28 views

Work out percentages and commisions

I have a price 265.69 top price. Of this 265.69, 180.83 is cost. 45 is profit 13.29 is a commission at 5% of price and 26.57 is another commission at 10% of the price 180.83 + 45 + 13.29 + 26.57 = ...
1
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1answer
16 views

Trigonometry graphs sinusoidal waves

i need help on this questions. I couldn't figure how to determine for both question A and B. But i have the answers for them, i just don't understand how the amplitude is 3 and so on.
2
votes
4answers
127 views

If $\omega + 1 = \omega$, find $\omega$ ($\omega \not= - \infty$ or $\infty$)

If $\omega + 1 = \omega$, find $\omega$ ($\omega \not= - \infty$ or $\infty$). It does not have to be a real number. My teacher gave us this question just to play around with, and my first ...
-3
votes
1answer
32 views

Pipe A is a inlet pipe filling the tank at 8000 litre/hour .Pipe B is the outlet pipe which empties the tank in 3 hours. [on hold]

Pipe A is a inlet pipe filling the tank at 8000 litre/hour . Pipe B is the outlet pipe which empties the tank in 3 hours.The capacity of the tank is?
1
vote
2answers
32 views

Interesting Functional Equations Problem?

Find all functions $f:\mathbb R \to \mathbb R$ that satisfy $f(x) + 3 f\left( \frac {x-1}{x} \right) = 7x$. How would we solve this? I noticed that if you plug in $\frac{x-1}{x}$ in for $x$, and ...
8
votes
4answers
80 views

Finding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$

I need help understanding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$ or $\displaystyle \sum_{i=0}^{180} \sin(i)$ This might be related to a formula to find ...
0
votes
1answer
24 views

Linear Algebra Analytical Exercise

This one has me stumped... $$H=C(sI-A)^{-1}B$$ and $$H_{CL} = C(sI-A+BK)^{-1}BG$$ Show that $$H_{CL} = H[I+K(sI-A))^{-1}B]^{-1}G$$ Any hints would be greatly appreciated!
0
votes
1answer
14 views

Geometric progression in annuity

I am working on the following problem that involves annuity which deposits form a geometric progression. Stan elects to receive his retirement benefit over $20$ years at the rate of $2,000$ per ...
-5
votes
4answers
60 views

Tea with grandmother [on hold]

My mother still makes tea with the old saying: one spoon per person and one for the pot. We used to buy a packet of tea every week but since grandmother came to live with us we have to buy two packets ...
0
votes
2answers
36 views

Mathematics and logs

For this indirect utility function: v(y) = ln(1/3 y) + 2 ln (2/3 y) = 3 ln(y) + ln (4/27) How did they simplify to 3 ln(y) + ln (4/27)? Im a bit confused, if there is a site helping with this ...
-1
votes
3answers
34 views

Why examples of the order of algebraic computations do not agree with calculator results?

This my first lesson in Algebra I replaced the dot signs with x. I've never seen times done with a dot before Lesson taken from MathPlanet Operations in the correct order When you are faced with a ...
7
votes
2answers
59 views

Function composition: $f^{653}(56)=?$

Let $f(x) = \frac1{(1-x)}$. Define the function $f^r$ to be $f^r(x) = f(f(f(...f(f(x)))))$. Find $f^{653}(56)$. What I've done: I started with r=1,2,3 and noticed the following pattern: $$f^r(x)= ...
0
votes
0answers
9 views

Calculating the interest rate for an annuity (Exam FM)

I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following. $X$=monthly payment , $i$=effective ...
-1
votes
1answer
30 views

Factoring/Expansion explantion

Sorry if I call something by the wrong name since I didnt learn math in english. ok so for example this: (a+b)(a-b) if you break it down to the second "()" you will end up with this: a+-b could ...
0
votes
2answers
46 views

Why is $y{(\log_a(x))} = \log_a{(x^y)}$?

Why is $y{(\log_a(x))} = \log_a{(x^y)}$? I feel like I'm missing something here. Sorry if I put the title wrong..
1
vote
2answers
31 views

Trouble understanding algebra in induction proof

I'm on hour 20 of studying for the discrete math midterm tomorrow, and I've got to be honest I'm a little panicked. In particular I'm having trouble with induction proofs, not because I don't ...
1
vote
1answer
24 views

Remainder theorem thinking question given properties of the original equation

Consider a cubic polynomial function $y=f(x)$ with the following properties: $f(x) \ge 0$ only for $x=-1$ and $x\ge3$ when $f(x)$ is divided by $(x-4)$ the remainder is $50$. Find the equation ...
7
votes
4answers
1k views

Confusing algebra rule: why $\frac{7^{n+1}-1}{6} + 7^{n+1} = \frac{7^{n+2}-1}{6}$?

Math rule I don't understand. Hey guys, my discrete math midterm is tomorrow and I'm studying proof styles. I came across a rule (algebra maybe?) I don't quite understand and I was hoping someone ...
1
vote
2answers
24 views

How to solve higher grade polynomials of complex numbers $q^{10}-2q^5+2=0$

If I wanted to find the roots for $q^{10}-2q^5+2=0$, how would I go about doing that? I tried treating it like a quadratic equation, but couldn't get there. I also tried putting $q=(a+ib)$ but that ...
0
votes
1answer
23 views

between what two disjoint sections we can do a unification in order to get this group of solutions?

between what two disjoint sections we can do a unification in order to get this group of solutions? $0<|x+6|\leq{0.4}$ in other words, in what values should I fill the blankets: (____,____) ...
3
votes
3answers
53 views

How can I find the point where two algebraic equations, in the form $y=mx+b$, intersect without graphing?

Suppose I have these two algebraic equations in the format $y=mx+b$: $$ y=2x+4 \\ y=3x+5 \\ $$ Now, by graphing these two algebraic equations on a coordinate plane, I find that they intersect at the ...
5
votes
3answers
101 views

Solve $x^3 - x + 1 = 0$

Solve $x^3 - x + 1 = 0$, this cannot be done through elementary methods. Although, this is way out of my capabilities, I would love to see a solution (closed form only). Thanks!
-1
votes
2answers
98 views

What is the formula to generate this number sequence : 1 , 7 , 14, 30

What is the formula to generate this number sequence : 1 , 7 , 14, 30 I'm sure this is very simple for you guys. But it's got me alittle stuck. Thanks To clarify, I'm not an advanced maths student. ...
2
votes
1answer
34 views

Solving $z^2-2iz+1=0$ in complex numbers

Solve: $z^2-2iz+1=0$ I did: $$(z-i)^2-(i)^2+1=0$$ $$(z-i)^2+2=0$$ $$((z-i)-\sqrt{2})((z-i)+\sqrt{2})$$ but that's wrong. Why?
1
vote
5answers
112 views

Sum of $1+2+4+8+…$ [duplicate]

I was solving a recurrence problem which had a sequence such as $y = (1+2+4+8+...)\sqrt n$, and I wanted to find what $x = 1+2+4+8+...$ was. So consider $x = 1+2+4+8+...$ as an infinite series. $$x-1 ...
0
votes
2answers
23 views

Factoring Polynomial with Complex Coefficients - Cauchy's Theorem

I'm faced with another polynomial (with complex coefficients) that I seem to only know how to solve using wolfram alpha. Here is the original integral that I need to compute using algebra and Cauchy's ...
1
vote
1answer
29 views

Irrational numbers and proving constant functions

Let $f:\mathbb R \to \mathbb R$ be a function such that for any irrational number $r$, and any real number $x$ we have $f(x)=f(x+r)$. Show that f is a constant function. How would we go about solving ...
1
vote
4answers
33 views

Basic Math, exponents and algebra

I have the equation $$\frac{x_1^{-\frac{1}{2}}}{{x_2^{-\frac{1}{2}}}} = p_l/p_2$$ How do I get $x_2$ on its own? I have $$x_2^{-\frac{1}{2}} = \frac{p_2(x_1^{-\frac{1}{2}})}{p_1}$$ And if you have a ...
0
votes
1answer
14 views

Quick question on relative minima/maxima of a cubic function

I need help with #36 on this page. Is there a way to solve without looking at the graph? Thanks!