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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0answers
104 views

Evaluate this product $n \times \frac{n-1}{2} \times \dots \times \frac{n-(2^k-1)}{2^k}$

For $k = \lfloor \log_{2}(n+1) \rfloor - 1$ evaluate $n \times \frac{n-1}{2} \times\frac{n-3}{4} \times \frac{n-7}{8} \times \dots \times \frac{n-(2^{k}-1)}{2^k}$ So the product goes up to $k$ and I ...
0
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3answers
31 views

Describe to me what is happening here (Pre-algebra)

I get confused on the second step. Can someone describe to me what is happening? If I want to solve this, what should the first thing I look at in my head such that I get the correct answer in the ...
3
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2answers
41 views

Trigonometry sum of solutions question

Problem: For which $a$ will the sum of solutions be equal to $100$, in $\sin(\sqrt{ax-x^2})=0$. The attempt at a solution: For $\sin(x)=0$, $x$ must be equal to $0$, so we get ...
0
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1answer
18 views

solving the number of boys who are left handed

In a group of 45 children, 60 percent of the children are boys, and 60 percent of the children are left-handed. If I want to solve the number of boys who are left handed then will it not be ...
5
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2answers
82 views

Fermat's Last Theorem for Negative $n$

While studying Fermat's Last Theorem and Pythagorean triples, the following question occurred to me: For the equation $a^n+b^n=c^n$, where $n$ is a negative integer, a) does a solution exist, and b) ...
0
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1answer
23 views

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept.

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = (1/5)x^4(x^2 - 3) the choice 1- 0, ...
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3answers
58 views

The real cubic root expression

$2x^3-2x^2-3x+2=0$ has 3 real root, but they are all express in such way: $x=\dfrac{1}{3}\left(1+\dfrac{\sqrt[3]{-23+3i\sqrt{237}}}{\sqrt[3]{2^2}}+\dfrac{11}{\sqrt[3]{2(-23+3i\sqrt{237}})}\right)$ ...
0
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1answer
29 views

shortest distance between the point $(0,-3)$ and the curve $y=1+a_{1}x^2 + a_{2}x^4 + …+a_{n}x^{2n}$

If each $a_{i}>0,$ Then the shortest distance between the point $(0,-3)$ and the curve $$y=1+a_{1}x^2 + a_{2}x^4 + \cdots +a_{n}x^{2n}$$ is $\bf{My\; Try::}$ Let $P(x,y)$ be ant point on the ...
0
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4answers
60 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 ...
0
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2answers
31 views

Angle Measure: Angles in Standard Position, is it a useless term?

I have a pre calculus test next week, and I have been going over the chapters to gain a deeper understanding; however, I find it difficult, or at least I find the concept of "Angles in Standard ...
0
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1answer
19 views

How can I determine the row index of a parking space?

This represents a parking lot with 7 rows, containing a total of 392 spaces: In the example above, the row indexes from left to right would be: ...
0
votes
1answer
33 views

Rational Inequality Question

Is my process correct? Solve: $\dfrac{x-3}{x+5}\leq3$ $$\dfrac{x-3}{x+5}-\dfrac{3(x+5)}{x+5}\leq0$$ $$\dfrac{x-3-3x-15}{x+5}\leq0$$ $$\dfrac{-2(x+9)}{x+5}\leq0$$ $$\dfrac{x+9}{x+5}\geq0$$ ...
2
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1answer
33 views

Trigonometric identity proof problem

My problem is from Israel Gelfand's Trigonometry textbook. Page 48. Exercise 5: d) $\frac{\sin\alpha}{1+\cos\alpha}=\frac{1-\cos\alpha}{\sin\alpha}$ I would appreciate some hints on how to ...
0
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2answers
52 views

The best way to factorize?

$f(t) = t^3 -t^2 +t + 7$. Just made it up, but looking through previous tests, they come up a lot when trying to find eigenvalues. How would I easily factorize this or make it=0? Wow, thanks for the ...
1
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2answers
103 views

Omitting $i$ in calculations

Is it possible in various calculations related to the complex plane which also include analytic geometry , calculating distances etc, to omit $i$ and treat the imaginary axis as simply the cartesian ...
1
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2answers
54 views

How to find out number of real solutions to this without graphing?

$$ 3^x = 4x^2 $$ My prof's notes just says to look at the graph and you'll see that they intersect in 3 points. But is there another way of doing this if you can't graph it?
6
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1answer
69 views

What am I doing wrong in this algebra excercise?

This is my first question here, so please forgive me if the format etc. are not quite right. I've been attacking an algebra question, and my workings are below. There's a mistake somewhere (I don't ...
0
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1answer
30 views

What is the domain? [closed]

What is the domain of the function $f(x) = \sqrt{4 x + 37}$? I am not sure where to get started with this problem. Thanks in advance!
2
votes
3answers
88 views

Solve exponential equation $3^x= 2^x+2$

How do we solve this? I can't think of an easy way.. Is there any way to solve it without using newton's method or other approximations? $3^x=2^x+2$
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1answer
34 views

SAT and deceptive graphs (figure not drawn to scale)

Question I. Figure may be found at: https://www.dropbox.com/s/skkkx9ydnrsdq8o/20140709_153701.jpg The Venn diagram above represents the 20 students who took one or more of the three available art ...
0
votes
0answers
16 views

bounds of solution to the system of nonlinear equations

I have a system of nonlinear equations: \begin{eqnarray*} F_1(x,y) &=& 0,\\ F_2(x,y) &=& 0, \end{eqnarray*} where $F_i(x,y)$ with $i=1,2$ are continuosly differentiable in $(x,y)$. ...
3
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3answers
56 views

Solve $\dfrac{x}{x-2}>2$ by first rewriting it in the form $\dfrac{P(x)}{Q(x)}>0$

Edit: So then is this the correct final solution? $x<4,(\infty,4), x\ne2$ I am asked to do this: Solve $\dfrac{x}{x-2}>2$ by first rewriting it in the form $\dfrac{P(x)}{Q(x)}>0$ ...
2
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3answers
51 views

Square root of a squared number changes sign, which to apply first?

Heres something Ive always found interesting. Supose we have a variable $x$, and $x$ equals a negative number: Say: $$x=-17$$ Now, I can apply a square to both sides of the equation and preserve ...
0
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1answer
25 views

simplify following 4y+6x divided by xy

simplify: 4y+6x/xy I did 4y*xy = 4xy^2 and 6x^2y / xy I then /xy = 4y+6x = (2) 2y+3x. But this was not correct. Help in steps please.
0
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2answers
36 views

SAT Algebra and elementary number theory

Question 1. If $a>5$ and $b>4$, then which of the following must be true? i. $a>b$ ii. $a+b>9$ iii.$a+b>11$ I think all 3 are true, but the answer is ii. only. Question 2. ...
0
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3answers
53 views

Find the range of (x+1)/(2x+1)

I recently encountered with this question in an exam, but wasn't able to solve it. At first I equated the og eqn to y and created an eqn in y, but that didn't help. any hint?
1
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1answer
32 views

consider a square of side length $x$, find the area of the region which contains the points which are closer to its centre than the sides.

Any ideas how to start. I am having trouble figuring out the region itself All ideas are appreciated thanks
2
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0answers
31 views

AMM Polynomial equation

Solve the equation: $x^7+7px^5+14p^2x^3+7p^3x+q=0$ I've tried obvious things like factorization or maybe guessing a solution. I'd appreciate a solution not too far from high school level.
0
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0answers
5 views

tangent vector on cone

Suppose that $C$ is a cone with vertx at the origin and let $\nu(x)= (\nu_1(x),\cdots, \nu_n(x))$ is the tangent vector at the point $x \in \partial E$. Is $\nu(x)$, (as function of $ x \in \partial ...
1
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2answers
46 views

Find the exact value of the trigonometric function $\sin 7\pi/ 6$

I am finding it a little difficult to solve this problem. The reference angle for $\sin 7\pi/6$ is sin 30 degrees (I think) which is sine 1/2. But that is not the answer. How do I sove this problem?
0
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0answers
21 views

How to find a certain uppper bound (see details)?

What would be the most efficient way to find this upper bound? Given natural number n and a natural number d < n, find the ...
0
votes
6answers
107 views

Given that $i$ is a root of: $P(x)=x^4 + 2x^3+ 3x^2 + 2x+2$ find all the other roots

I have a simple question here but I don't know how to solve it. Given that $i$ is a root of: $P(x)=x^4 + 2x^3+ 3x^2 + 2x+2$ find all the other roots. Help is much appreciated. Thanks.
0
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2answers
64 views

Simplify: $\displaystyle\frac{\frac{a}{x}-\frac{a}{y}}{\frac{a}{x}+\frac{a}{y}}$ [duplicate]

Simplify: $\displaystyle\frac{\frac{a}{x}-\frac{a}{y}}{\frac{a}{x}+\frac{a}{y}}$ I did $\displaystyle\frac{ay}{xy}-\frac{ax}{xy}=y-x$ on top in underside. I did ...
0
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3answers
53 views

equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$

Frist I solved this equation $\displaystyle \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{xy}}$ by multiplying $xy \left(\frac{xy}{x}+\frac{xy}{y}\right)=y+x$ The answer is correct. Next equation was: ...
1
vote
5answers
85 views

Solving $\sin x = 4\sin10°\sin40°\sin(70°-x)$

So, I have this equation: $$\sin x = 4\sin10°\sin40°\sin(70°-x)$$ And I'm trying to solve for $x$. Apparently $x=20°$ is the (smallest positive) solution but I can't arrive at it. I'm not very ...
1
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3answers
31 views

Solving for the value inside a base 10 logarithm

I have an equation of $\log(d)=(-x-A)/(10n)$ that I need to solve for $d$. How do I "reverse" the logarithm to obtain $d$? I apologize if this is super easy, I just can't even figure out how to Google ...
7
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1answer
64 views

Find the maximum value of $ \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1} $

If $x\in\mathbb{R}$ find the maximum value of $$ \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1} $$ I tried this: Let $$y= \sqrt{x^4-3x^2-6x+13} - \sqrt{x^4-x^2+1}$$ For maxima ...
0
votes
2answers
29 views

Simplify: $\frac{3x}{x+2} - \frac{4x}{2-x} - \frac{2x-1}{x^2-4}$

Simplify $$\frac{3x}{x+2} - \frac{4x}{2-x} - \frac{2x-1}{x^2-4}$$ First I expanded $x²-4$ into $(x+2)(x-2)$. There are 3 denominators. So I multiplied the numerators into: ...
0
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0answers
31 views

Using Algebra with Trig Functions

Using Algebra with Trig Functions I'm trying to find the correct 1 second audio signal I would need to apply to a 1 second known noise signal to have the output signal be a sin wave. The basic ...
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2answers
24 views

A rectangular photograph is twice as tall as it is wide.

A rectangular photograph is twice as tall as it is wide. When a 4 cm wide frame is placed around the photo, the area of the frame and photo equals three times that of the photo alone. The original ...
4
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4answers
79 views

How to solve: $\frac{2^{n+1}}{n+1}=\frac{4+2^n}{3}$

$n$ is an integer variable satisfying $$\frac{2^{n+1}}{n+1}=\frac{4+2^n}{3}$$ How can I find $n$?
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1answer
136 views

Quick complex number proof question:

How would I go about proving the following identity: $$\frac{1}{\left|z\right|} = \left|\frac{1}{z}\right|$$ I keep finding myself going in circles. I've tried using this identity: $|z|^2 = z^*z$ ...
1
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2answers
41 views

Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ.

Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ. How do I solve?
0
votes
1answer
13 views

Drawing a graph based on derivative properties

I'm just doing some math and I could use some help. The problem asks me to draw a graph based on the following properties: $f'(x) > 0$ if $\lvert x\rvert < 2$ $f'(x) < 0$ if $\lvert x\rvert ...
2
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2answers
32 views

Can someone please check my answer for this exponential question?

Would someone mind helping me by checking my answer that I have worked out? I think I am correct... but I can't seem to find an answer for it anywhere so I want to be sure I am right. Thank you in ...
2
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2answers
171 views

Fractional exponents - adding the exponent?

I have this question for which I need to simplify the expression so that only positive exponents occur, and assuming the variables are positive: $$x^{2/5} x^{1/4} x^{-1/2}$$ The answer is supposed ...
3
votes
2answers
51 views

Trigonometry calculation problem

Problem: Calculate $\cos(\alpha+60)$, if $\sin(\alpha)=\frac{2}{3}$ and $\alpha\in[90^\circ,180^\circ]$. I have tried following: ...
1
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1answer
40 views

A heavy simplification

$$-\frac{\sum _{i=1}^{m-1} 2^{i-1} \left(\binom{m}{i-1}-3^{m-i}\right)}{m-1}==2^{m-1}$$ Is there a way to show that this equation makes a true statement? I am somehow stuck here
0
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1answer
37 views

Expansion of $(1+px+qx^2)^8\equiv 1+8x+52x^2+kx^3$…

$(1+px+qx^2)^8 \equiv 1+8x+52x^2+kx^3...$ Given that expression, calculate the values of p, q, and k. I'm guessing this is a trinomial that needs to be turned into a binomial, but how would you do ...
2
votes
1answer
36 views

Using the definition of a derivative

I'm here with a maths problem. I'm trying to find the derivative of an expression but when I calculate it I get different answers depending on if I use the power rule or definition of a derivative. ...