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
1
vote
3answers
32 views
How should I go about this approaching-infinite limit problem?
I'm doing some exercises of limits approaching infinite, most are simple polynomials where only the highest degree term will matter in the end but for this one I couldn't find a solution (not correct ...
1
vote
1answer
29 views
Linear Approximation
I have an exercise, giving this question.
Find the linear approximation $Y$ to $f(x)$ near $x=a$.
$$
f(x) = x + x^4,\quad a=0
$$
I can see in my result list that it says $Y=x$, however, after ...
0
votes
1answer
26 views
Tell me the ideal selling price to get back a specified number
If I am buying something at xxx,
what is the price to sell it if I want a profit of $2.50 after minus-ing 0.63% (broker fee) from the selling price?
I need to make this into an excel formula, but ...
0
votes
2answers
46 views
Solve this system of equations
Solve this system of equations
$$a+b = 3 -c$$
$$\frac{1}{a}+\frac{1}{b}= \frac{5}{12}-\frac{1}{c}$$
$$ a^3+b^3 = 45 -c^3$$
0
votes
2answers
27 views
How to find the minimum value of the expression? $\sqrt{(x-0,5)^2+0,75}+\sqrt{(x-\frac{\sqrt{3}}{2})^2+0,25}$?
What is the minimum value of this expression $\sqrt{(x-0,5)^2+0,75}+\sqrt{(x-\frac{\sqrt{3}}{2})^2+0,25}$ ?
0
votes
3answers
65 views
Finding the number of integer solutions, why is this wrong?
The question is to find the number of solutions such that $(x, y)$ are integers: $(x-8)(x-10)=2^y$. Here's what I did: $u(u-2)=2^y$. From the quadratic formula, $u=1+\sqrt{1+2^y}$. This is where I ...
-1
votes
1answer
39 views
How find this $(8\sqrt{6}-12\sqrt{2})\left(t_{2}+160e^{-\frac{1}{160}t_{2}}-1\right)=15$ [closed]
someone can help me?
use MATLAB find $$(8\sqrt{6}-12\sqrt{2})\left(t_{1}+120e^{-\frac{1}{120}t_{1}}-1\right)=20$$
and
$$(8\sqrt{6}-12\sqrt{2})\left(t_{2}+160e^{-\frac{1}{160}t_{2}}-1\right)=15$$
I ...
2
votes
1answer
28 views
f(n) for rows with $2^x$ bits on
This is similar to a question I asked here but now I need to alter it so I have brought across the relevant parts.
Given a binary table with n bits as follows:
$$\begin{array}{cccc|l}
...
6
votes
3answers
62 views
How do I factor this?
How do I factor $p^2+8pq+16q^2-9r^2$? I know how to group the first two terms, but I dont know what to do with the other half. Can someone help me with this problem?
12
votes
6answers
625 views
If $2^x=0$, find $x$.
If $2^x=0$, find $x$.
Solution: I know range of $2^x$ function is $(0,\infty)$.
So $2^x=0$ is not possible for any real value of $x$
Hence, equation is wrong. We can't find value of $x$. Am I ...
2
votes
3answers
52 views
Algebra Equation with equals on left hand side
$6 = 4 - 2x =$
Show the answer with the mechanics of working out.
2
votes
1answer
38 views
If $y<x$ is there a way to phrase it in terms of $y>$something?
For instance I know $y<x$ implies $-y > -x$ but is there a way to phrase it in terms of $y>$ something (that does not itself contain $y$)?
5
votes
4answers
67 views
Where does the function $f(x) = \frac{2x}{x - 7}$ have an increasing slope?
Where does the function $f(x) = \frac{2x}{x - 7}$ have an increasing slope?
$a. x \le 0, x > 7$
$b. x<7$
$c. x > 7$
$d. x \in \Bbb R, x \neq 7$
This question is from a test of mine in a ...
5
votes
3answers
47 views
Algebraic expression in its most simplified form
I am trying to simplify the algebraic expression:
$$\bigg(x-\dfrac{4}{(x-3)}\bigg)\div \bigg(x+\dfrac{2+6x}{(x-3)}\bigg)$$
I am having trouble though. My current thoughts are:
...
1
vote
2answers
49 views
How to solve this system of equation.
$x^2-yz=a^2$
$y^2-zx=b^2$
$z^2-xy=c^2$
How to solve this equation for $x,y,z$. Use elementary methods to solve (elimination, substitution etc.).
Given answer is:$x=\pm\dfrac{a^4-b^2c^2}{\sqrt ...
1
vote
0answers
27 views
Inverse function of product of exponential matrices
I am looking for the value of $\mathbf{X}$ in a function of the type
\begin{align}
(\mathbf{X}-\mathbf{A})e^{\mathbf{X}}e^{-\mathbf{A}} = \mathbf{B}
\end{align}
where ...
5
votes
3answers
91 views
How to solve this simultaneous equation of $3$ variables.
I've stuck in this equation system.No clue how to start ?
$x+y+z=a+b+c\,\cdots(1)$
$ax+by+cz=a^2+b^2+c^2\,\cdots(2)$
$ax^2+by^2+cz^2=a^3+b^3+c^3\,\cdots(3)$
Find the value of x,y,z is in the form ...
1
vote
3answers
47 views
Which one is the correct series expansion?
Is
$$p^{n+1} = p^0+p^1+ \dots + p^n$$
or
$$p^{n+1} = p^0\times p^1\times \dots \times p^n\text{ ?}$$
I am confused.
please explain the correct one.
0
votes
1answer
22 views
I need help with a word problem .
The length of a rectangle is 1 meter less than twice its width. If the area of the rectangle is 120 square meters, find the dimensions of the rectangle
0
votes
1answer
37 views
How do I solve this solution-mixing problem?
A chemist has a 55% acid solution and a 40% acid solution. How many liters of each should be
mixed in order to produce 100 liters of a 46% acid solution?
1
vote
2answers
36 views
Equation of a line passing through a point and forming a triangle with the axes
How can I find the equation of a line that;
is passing through the point (8, 6) and
is forming a triangle of area 12 with the axes
?
So I tried to start using $A = |{\frac{mn}{2}}|$ and ...
1
vote
2answers
40 views
System of equations word problem
Andrea's Sequoia gets 12 miles per gallon while driving in the city, and 20 miles per gallon while on the highway. The last time she filled up the car it took 16 gallons of gas, and she had driven 280 ...
1
vote
1answer
26 views
Like term reduction
In finding the derivative of $f(x) = 4x - x^2$ we first find the difference of the numerator $f(x + h) - f(x)$. Therefore we have $f(x + h) = 4(x + h) - (x + h)^2 = 4x + 4h - x^2 - 2xh - h^2$ minus ...
4
votes
6answers
118 views
Solving $\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$
Where do I start to solve a equation for x like the one below?
$$\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$$
After squaring it, it's too complicated; but there's nothing to factor or to ...
4
votes
1answer
45 views
Is it possible to rationalize a denominator containing two cube roots?
The fraction in question is
$$-\frac{12}{\sqrt[3]{12\sqrt{849} + 108} - \sqrt[3]{12\sqrt{849} - 108}}$$
And was reached in calculating the solution to $x^4 - x - 1 = 0$. I've tried all the standard ...
2
votes
2answers
59 views
How do I solve $x^2 + y^2 + xy = z$ for $y$
How do I solve the following equation for $x$ or $y$ (does not matter because you can swap them):
$$
x^2+y^2+xy=z
$$
1
vote
1answer
38 views
How do you solve for Y?
I know there has got to be a way to solve for $Y$ but I just can't seem to figure it out. Does anyone know how to solve this? Please help :)
$$5(Y(8))=C$$
$$C(Y(4))=B$$
$$B(Y(2))=A$$
...
3
votes
4answers
68 views
Solve equation $\sqrt{s+13} - \sqrt{7-s} = 2$
Solve the equation
$$\sqrt{s+13}-\sqrt{7-s} = 2$$
I moved the $-\sqrt{7-s}$ to the right side
Thus, I had
$$\sqrt{s+ 13} = 2 +\sqrt{7-s}$$
I then squared both sides
$$\sqrt{s+ 13}^2 = \left(2 ...
0
votes
0answers
15 views
Find the terminal point when the distance is not in terms of $\pi$
From Stewart Precalculus 5th edi, P407
I am not sure what to do here, in the textbook, Steward didn't provide any example as to finding the terminal point when the distance $t$ is an integer. I ...
1
vote
1answer
50 views
For which values is $x^3$ less than or equal to $3x$?
The title says it all. The answers say:
$x\le -\sqrt{3}$ and $0\le x\le \sqrt{3}$
(can someone edit this so all the $<$ have an 'or equal to' sign. Edit the roots as well please.
I'm not sure ...
1
vote
1answer
21 views
Number of equivalent rectangular paths between two points
I am trying to determine the number of paths between two points.
I am representing the paths as a list of steps "ruru" = right -> up -> right -> up
For my purposes, we can assume that there will ...
0
votes
0answers
42 views
Quaternion exponential map, rotations and interpolation
A code snippet I need to optimize is performing something peculiar. It seems that it's somehow related to transforming from a frame of reference to another. This is what it does, in mathematical ...
12
votes
3answers
118 views
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$
Here is a statement that seems prima facie obvious, but when I try to prove it, I am lost.
Let $x_1 , x_2 \dots x_k$ be complex numbers satisfying:
$$x_1 + x_2 \dots + x_k = 0$$
$$x_1^2 + x_2^2 ...
3
votes
3answers
74 views
Determining $\sin(15)$, $\sin(32)$, $\cos(49)$, etc.
How do you in general find the trigonometric function values? I know how to find them for 30 45, and 60 using the 60-60-60 and 45-45-90 triangle but don't know for, say $\sin(15)$ or $\tan(75)$ or ...
2
votes
0answers
47 views
Is there any easy way to simplify the following term?
$[p\times (p+1)\times (p+2)\times (p+3)\times (p+q)^3] - [4\times p^2\times (p+1)\times (p+2)\times (p+q)^2\times (p+q+3) ] +[6\times p^3\times (p+1)\times (p+q)\times (p+q+2)\times (p+q+3)] -[3\times ...
1
vote
1answer
30 views
Is this enough info to solve this time dilation problem
There are two clocks. One is a regular clock measuring regular time $\tau$. The other is a clock measuring time $t$ which also advances clockwise, but does not advance uniformly--it accelerates ...
-1
votes
1answer
45 views
If 3 out of 5 randomly chosen reports used incorrect style, how many to expect out of 125
A teacher randomly reads 5 written reports from the 125 she has to grade. He finds that 3 reports did not follow the correct style. At this time same rate, how many of the 125 can she expect to not ...
3
votes
1answer
45 views
How to solve these elementary algebra questions?
Lionel is thinking of two numbers. The sum of twice the larger number and 4 times the smaller number is 40. Twice the smaller number is 4 more than larger number. Find the larger number.
Mrs tan ...
2
votes
1answer
27 views
Need help with algebra portion of calculus finding slope of secant line
The example problem is: Given f(x) = $x^2$,find and simplify the slope of the secant line for a = 1 and h = any non-zero number.
The answer is as follows:
For a = 1 and h any non-zero number, the ...
-10
votes
1answer
60 views
Nate's older brother! [closed]
Nate's older brother Mickey has been looking for an old used car just to drive to work. An advertisement in the paper is offering a car listed at $899.95 for sale at 25 percent off. The best estimate ...
-1
votes
3answers
44 views
question about percentages
At the start of the new year, the price for a gallon of milk at a local grocery store increased by 2.4% as a result of inflation. If a gallon of milk cost $2.92 last year, about how much does it cost ...
4
votes
3answers
174 views
how to solve this multivariate quadratic equation?
Any hope to acquire an analytic solution to such equations:
Solve:
$$\sum_{j=1}^n a_{ij} x_i x_j = b_i$$
for $i=1,\ldots,n$, where $a_{ij}$'s and $b_i$'s are known constants and $x_i$'s are unknowns ...
2
votes
1answer
50 views
what is $\lim_{x\to6}\frac{5}{(x-6)^2}$
$$\lim_{x\to6}\frac{5}{(x-6)^2}$$
Is it undefined or infinity and why ?
1
vote
1answer
60 views
How are these inequalities simplified?
How does this:
(a > b && a > c && b <= c) ||
(a > b && a <= c && b < c)
simplify down to this:
...
3
votes
2answers
162 views
Does this polynomial factorize further?
I just did a national exam and this question was in it; I am convinced this does not work:
Given that $(x - 1)$ is a factor of $x^3 + 3x^2 + x - 5$, factorize this cubic fully.
My attempt
1 | ...
1
vote
1answer
39 views
$p(x)$ and $q(x)$ be non-zero polynomials with real coefficients such that…
I am stuck on the following problem:
Let $p(x)$ and $q(x)$ be non-zero polynomials with real coefficients such that
degree$(p(x)) > \text{degree}(q(x))$. If the graphs of $y = p(x)$ and $y = ...
1
vote
1answer
32 views
What is orthogonal projection of zero to triangle generated by three points (0,1) (5,0) and (2,4)
What is orthogonal projection of zero to triangle generated by three points (0,1) (5,0) and (2,4)
Well, in my opinion, there is none. However, my teacher think that it has but he don't know how ...
1
vote
1answer
40 views
Does There Exist a Term for the Unique Nonpositive Square Root of a Nonnegative Real Number?
The term "principal square root" describes the unique nonnegative square root of a nonnegative real number.
Does there exist a term to describe the unique nonpositive square root of a nonnegative ...
1
vote
2answers
64 views
Solving a system of equation:
Solve for $x,y$:
\begin{align}
x^3 + y^3&=2\\
x^2 +x + 9y - 3y^2&=8 \\
\end{align}
I can find $x=y=1$ by guessing. Please help me solve it without using computer.
Thanks
Edited, sorry, I ...
3
votes
2answers
60 views
Solving 3 simultaneous cubic equations
I have three equations of the form:
$$ i_1^3L_1 + i_1K +V_1 + (i_2+i_3+C)Z_n = 0 $$
$$ i_2^3L_2 + i_2K +V_2 + (i_1+i_3+C)Z_n = 0 $$
$$ i_3^3L_3 + i_3K +V_3 + (i_1+i_2+C)Z_n = 0 $$
where $ ...
