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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1answer
74 views

A question on Time and Work

A takes $6$ days less than the time taken by $B$ to finish a piece of work. If both $A$ and $B$ together can finish it in $4$ days, find the time taken by $B$ to finish the work... I am not getting ...
0
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2answers
49 views

I'm having problem with this equation

So I was solving some determinant and got to this $(x-2)(x^2-4x+5)-(x-1)-(x-1)=0$. So I know there should be 3 solutions, and I know I can do like $x-2=0$ and $x^2-4x+5=0$ but what do I do with the ...
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votes
3answers
216 views

Suppose f and g are continuous functions such that $g(6) = 5$ and $\lim_{x\to6} [3f(x) + f(x)g(x)] = 40$. Find $f(6)$.

How in the world do I solve this? I am completely confused. Can someone please help me out?
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8answers
281 views

How to factor $9x^2-80x-9$?

How do I factor a trinomial like this? I'm having a lot of difficulty. How do I deal with the $9x^2$?
2
votes
5answers
85 views

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 ...
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1answer
34 views

Solving Three Part Ratio

I came across this question today and my Math 20-2 instructor expects that I know how to solve it. I have never seen a ratio like this before, I am usually using a ratio with 2 parts ($a:b = c:d$ or ...
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1answer
45 views

Bisection Method number of steps for convergence

For the bisection method, determine the formula $$n \geq \frac{\log(b_0-a_0)-\log(\epsilon)}{\log(2)}-1$$ for the number of steps to guarantee that $|{r-c_n}| < \epsilon.$ This is one of the ...
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1answer
35 views

Solving a random function?

If I have that $u_{2m}$ = ${2m\choose m}$ $2^{-2m}$ and $u_{2m-2}$ = ${2m-2\choose m-1}$ $2^{-2m+2}$ what would $u_{2m-2}-u_{2m}$ = ? I have tried writing it out explicitly and get a funny answer ...
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2answers
48 views

How to prove these equalities for $a,b,c \in \mathbb{C}$

I don't get what to do with problems such as these: Let $a,b,c \in \mathbb{C}$ so that: $a+b+c=0$, $a^2+b^2+c^2=0$ Prove $a^3=b^3=c^3$ and Let $a,b,c \in \mathbb{C}$ so that: $a+b+c=7$, ...
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1answer
25 views

Bounding the sum of “almost” factorials

I am analyzing the complexity of an algorithm and the result is the sum of n products. Product 1 is the factorial. Product 2 is the factorial divided by 2. Product 3 is the factorial divided by 3 etc. ...
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3answers
57 views

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 $t$?
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3answers
78 views

Find two consective odd numbers whose product is $1295$ [closed]

If the product of two consecutive odd numbers is $1295$, how can we find the two numbers?
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3answers
42 views

Solving simultaneous equations $2x = 1 - 3y$ and $3y^2 - x^2 = 2$

Someone please edit the question; also teach me to edit them! I'm new and I don't know how to do it! $2x = 1 - 3y$ $3y^2 - x^2 = 2$ Solve these simultaneous equations.
2
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1answer
56 views

Simple expression for this sum?

Is there any simple expression for the sum: $$ S = \sum_{n = 0}^{N-1} \frac{1}{a + e^{2 \pi i n / N}} $$ where $ N $ is a positive integer and $ a $ is some real number. It feels to me like there ...
-1
votes
1answer
26 views

How do I convert $x(-\frac { 1 }{ { 10 }^{ -r }-1 } -1)$ to $\frac { x }{ { 10 }^{ r }-1 } $

How do I convert the equation $$x\left(-\frac { 1 }{ { 10 }^{ -r }-1 } -1\right)$$ into this one: $$\frac { x }{ { 10 }^{ r }-1 } $$
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3answers
39 views

Graphing $-\log_2x$ , $\log_2(-x)$, and $-\log_2(-x)$ by hand.

Trying to graph $-\log_2x$ , $\log_2(-x)$, and $-\log_2(-x)$. I don't understand which one reflects over the x axis, the y axis?
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1answer
36 views

Sign problem in proof that $\Gamma'(1) = -\gamma$

Convergence of $(u_n)_{n \in \mathbb{N}} := \sum\nolimits_{k=1}^n \frac{1}{k} - \log(n)$ was proven before The egality $\Gamma'(1) = \lim_{n \to \infty}\int_0^n \log(t) (1-\frac{t}{n})^n dt$ was also ...
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2answers
58 views

What is the conjugate?

What is the conjugate? $\sqrt x +2 \sqrt b$ I'm not sure how to find the conjugate of any term. Help, please?
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2answers
193 views

A problem for math lovers to count the digits

Today a classmate of mine asked a question which is based on counting. Question. Find a positive integer which when multiplied up to $N$ times will give numbers having the same digits but differently ...
2
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0answers
32 views

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) ...
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3answers
92 views

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

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 ...
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2answers
24 views

Finding the reduction by percentage

So i kinda think i have figured this out, i'm not very good at math, and need a formula to figure out some stats for a game i'm playing. I have a Weapon with a reload speed of X sec.. however, i also ...
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2answers
60 views

Build the function by its values. Only combination of +, -, *, abs() allowed for this function.

I've decided to open a new, more common question about the simplest function f(1)=-1; f(2)=0; f(3)=1; f(4)=0.. So, here is the question. Let's say we have some function $y=f(x)$ we'd like to find by ...
2
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2answers
75 views

Need assistance on geometry problem

Having a really hard time solving this problem. Given: a circle of radius $a$ an ellipse with minor axis $g$ and major axis $f$ the ellipse is oriented so that the major axis is parallel with the ...
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2answers
41 views

Find coefficient of $x^8$ in $(1+x+x^2+x^3+…)^c$

Find coefficient of $x^8$ in $(1+x+x^2+x^3+...)^c$ Help me please I don't know what to do after that because of the exponent $c$
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0answers
56 views

Show that $v$ mod $2$ = $w$ mod $2$ if and only if $\alpha$ mod $2$ = $\beta$ mod $2$

Basic setting: 1) Let $N$ be an even integer, and $a$ and $b$ are two odd integers in $\mathbb{Z}_N$ such that $\gcd{(N, a)}=\gcd{(N, b)}=1$. Thus there exist $a^{-1}$ and $b^{-1}$ in ...
0
votes
2answers
70 views

Must $a$ be less than $b$ in the interval $[a, b]$?

If I describe an interval as $[a, b]$. Must $a$ be less than $b$? In my calculus book I read the definition of an integral of a function which is defined and bounded on $[a, b]$. And the area of the ...
0
votes
1answer
71 views

arithmetic and geometric progression

$a,b,c$ ,are consecutive arguments of a given arithmetic progression. $a^2, b^2, c^2$, are consecutive arguments of a geometric progression. With this information given, find the $q$ for the ...
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4answers
64 views

Solve $\frac3x - \frac4y = 1$ and $\frac7x + \frac2y = \frac{11}{12}$

How can we solve the following simultaneous equations: $$\frac3x - \frac4y = 1$$ $$\frac7x + \frac2y = \frac{11}{12}$$
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0answers
36 views

Equation involving a sum of radicals

How might one solve this equation analytically? $ \sqrt{6x^2-15x+7}+\sqrt{4x^2-8x-11}-\sqrt{2x^2-5x+5}= 2x-3 $
2
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1answer
17 views

How many unit cubes were used to create the large cubes?

The outside faces of a large cube are pointed . The large cube is then divided into unit cubes . There are exactly 125 unit cubes that have no paint . How many unit cubes were used to create the large ...
2
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2answers
56 views

How many sheep I have?

I divide my flock of sheep into two subflocks of different sizes. The difference between the sizes of the subflocks is equal to the difference between the squares of their sizes How many sheep do I ...
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2answers
53 views

How do i solve this literal equation? $V=\pi r^2h/3$ [closed]

I need some help on how to solve the following literal equation: $$V=\pi r^2h/3$$ for $h$.
0
votes
1answer
33 views

how to turn from one expressions to another, different expressions?

How to go from this expressions $$3(x-2)^{5/3}-5(x-6)(x-2)^{2/5}$$ to something simpler I was trying to go with common factor but it didn't seems to work...
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3answers
77 views

The graph of a function $y(x)$ is a straight line in a regular coordinate system if and only if $y(x) = ax + b$?

How does one prove: The graph of a function $y(x)$ is a straight line (no curves) in a regular coordinate system ($x,y$ coordinate system with axis' having interval $c$) if and only if $y(x) = ax + ...
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2answers
19 views

Different expressions…how to turn from one to another?

How to turn $$(x-2)^{-2/3}-{x\cdot(2/3)\cdot(x-2)^{-5/3}}$$ to $$\frac{x-6}{3(x-2)^{5/3}}$$ I did common denominator but with no use...
0
votes
2answers
125 views

How do you solve $5 \cos^2(x) + 6 \cos(x) = 8$?

Please help me! How do you solve $5 \cos^2(x) + 6 \cos(x) = 8$? My math teacher doesn't teach us very well and I need these! Someone Please teach me how to do this. Thank you!
0
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3answers
84 views

The ratio of two numbers is $7$ to $5$. The sum of the numbers is $24$. What are the numbers? [closed]

The ratio of two numbers is $7$ to $5$. The sum of the numbers is $24$. What are the numbers
1
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2answers
70 views

Solve for $X$: $4+2X > 7$

Solve for $$4+2x>7$$. My answer was 1 and 1/2 but I am not so sure it is right, could anyone confirm it for me. i need someone to solve the inequality. the first step would be to subtract $4$ ...
1
vote
6answers
162 views

How to factorize $2x^2+5x+3$?

I'm doing pre-calculus course at coursera.org and I'm in trouble with this solution $$2x^2 +5x +3 = (2x+3)(x+1)$$ By trial, using ac-method I got stuck: $$ ac = (2)(3) = 6\\ 6 + ? = 5 \Rightarrow~ ? ...
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2answers
94 views

Proof that $x^2 -3y^2 = 1$ has infinite solutions. ( x and y are integers)

I have to explain this to my brother who is in eighth grade and I would really love if you could tell this in simple terms (I'm no Maths guy).
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1answer
44 views

How to get the theta in this projectile equation?

The equation for the Parabolic Trajectory is $$y = x\tan{\theta}- \frac {gx^2}{2V_0^2\cos^2{\theta}}$$ It will be easy to get any variables if there's an angle, but how I can solve if the missing ...
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1answer
246 views

Representing whole numbers as $a^2 + b^2 + 4ab$ for integers $a,b$

Lets say it's $18$. Is there a way to be sure that this number can definitely be represented like $$a^2 + b^2 + 4ab$$ The problem mainly arises due to the $4ab$ and not $2ab$, otherwise only perfect ...
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3answers
56 views

the simplest function f(1)=-1; f(2)=0; f(3)=1; f(4)=0.

I'm looking for a function that gives f(1)=-1; f(2)=0; f(3)=1; f(4)=0. The other values are undefined and I don't pay any attention on them. The prefered ...
2
votes
2answers
428 views

If both integers $x$ and $y$ can be represented as $a^2 + b^2 + 4ab$, prove that $xy$ can also be represented like this …

There is a set $Q$ which contains all integral values that can be represented by $$a^2 + b^2 + 4ab$$, where $a$ and $b$ are also integers. If some integers $x$ and $y$ exist in this set, prove that ...
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vote
1answer
75 views

Find the radius of the tip of a die punch.

The following image shows a problem out of my math book, Trigonometry, by Michael Corral (problem 13, section 1.3 for those who may be interested). My analysis is that the $1.5$ (as far as I can ...
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1answer
26 views

Deriviation behind trigonometric equation

In an example of a trigonometry book I'm reading, I see the following operations performed on this equation $r = (r+3)\cos2.23^\circ$: $$ \\\ \\\ r = 3\cos2.23^\circ + r \cos2.23^\circ \\\ \\\ r ...
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1answer
49 views

Real Analysis basic questions

I am studying for math 400 lvl class and I forgot how one to one function on infinity value. For instance, consider the following: $$f(x)=tx+g, \hspace{1cm} -\infty < x < + \infty, \quad t,g, ...
2
votes
2answers
806 views

Equation of circle tangent to y=x and x-axis with radius 5

Find the equation of a circle in the 3rd quadrant that is tangent to the line y=x and the x-axis, with a radius of 5. One way I thought of doing it was letting the center point of the circle be ...
1
vote
1answer
56 views

how to simplify the following expression: $-(4i)^3$

How to simplify the following term $$-(4i)^3$$ I have tried solving it the following way: taking the square root of $-16$ to the third power and taking the negative of that. I am getting an answer ...