In mathematics education, precalculus or college algebra is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.
We can also write a general inequality ##x^2>a## where a is a number.
If ##x^2= a##, then ##x= \pm \sqrt a## which means ##x= \sqrt a## or ##\sqrt a##.
But in this case i don’t think it will be ##x > \pm \sqrt a## because if we take ##0## , it’s greater than a negative but in the original...
Problem statement : Let me copy and paste the problem as it appears in the text.
Attempt : From the "Relevant Equations" given above, we can compare to see that ##a1 = 1## and ##a^2+2=3##. These lead (after some algebra) to the three values of ##\boxed{a=0, \pm 1}##.
Issue : The book has...
I think the answer is an even function as the function ##x^2## is an even function and thus, is symmetrical w.r.t. Y axis. The question I have is how to do this problem algebraically. I tried to graph some functions on GeoGebra to verify my answer.
a) ##y = ln(x^2)##
b) ##y = sin(x^2)##...
It is clear that the terms of the sequence tend to zero when n tends to infinity (for some α) but I cannot find a method that allows me to understand for which of them the sum converges. Neither the root criterion nor that of the relationship seem to work. I tried to replace ##\sqrt[n]{n}## with...
This is the form of the function above:
I started by equating (1) to 1/2:
$$T(\varphi)=\frac{r^{2}+\tau^{2}2\tau\cos\varphi}{1+\tau^{2}r^{2}2\tau r\cos\varphi} = \frac{1}{2},$$
which can be rearranged to:
$$2r^{2}+2\tau^{2}1\tau^{2}r^{2}=2\tau\left[2r\right]\cos\varphi$$
using...
A balloon's volume is increasing at a rate of dV/dt. Express the rate of change of the circumference with respect to time (dc/dt) in terms of the volume and radius.
Homework Equations
Vsphere = (4/3)(π)(r^3)
C = (2)(π)(r)
The Attempt at a Solution [/B]
My strategy was to come up with two...
One of my homework questions said "Explain how to obtain f(x)=(3+x)^2+1 from the graph of y=x^2."
I know somehow you need to move the graph right 3, reflect about the xaxis, and move up one, but I don't know how to factor and manipulate the equation to show this.
Homework Statement
"Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x3 at the point B(3,3). (Picture of the graph: https://imgur.com/a/0wAnqcU)
Homework Equations
Here's a link: https://imgur.com/a/y71Z9GY
The Attempt at a Solution
Soo, I've...
One of our homework problem asks:
If f is a onetoone function such that f(3)=5 , find x given that f^1 (5)=3x1.
Here's how I attempted to solve the problem:
3=3x1
3x=2
x=2/3
Is this the correct way to solve the problem?
Homework Statement
Homework Equations
The Attempt at a Solution
I know I would have to do something with my calculator and I tried to solve like solving an equation for C, but not sure. I put all the matrices in my calculator. I then subtracted the first matrix to the other side then...
Homework Statement
Given that vector a = (1, 2, 5), b = (12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0
Homework Equations
No specific equations, as the question asks for the value without making any calculations. This problem...
My question is about basic algebra. I am thinking about the "why" here and I'm looking for an intuitive answer.
If you have the following equations:
=>S+U=90
=>S+U=90
and
=>40S+25U=2625
=>40S+25U=2625
you can then rewrite S=90−U and then substitute.
Now you have a single equation with one...
Hello,
Just to give you some background info, I'm a software developer looking to make a career switch to Mechanical Engineering (At least I think so). My interests lie in design, complex systems, maglev, rockets and new forms of space propulsion. Before I really commit myself to University, I...
Homework Statement
[/B]
"An airplane is flying on a bearing of 340 degrees at 400mph. A wind is blowing at a bearing of 320 degrees at 30mph. Find ground speed and direction of the plane."
Homework Equations
vx=vcosϕ
vy=vsinϕ
The Attempt at a Solution
[/B]
First, my teacher told us to change...
Homework Statement
A colony of ants will grow by 12% per month. If the colony originally contains 2000 ants how long will it take for the colony to double in size?
Answer  6.12 months
Homework Equations
A = P(1+r/n)nt
The Attempt at a Solution
r = 12% = 0.12
n = 12
P = 2000
A = 4000
t = ...
Homework Statement
Sketch the graphs of the following functions and show all asymptotes with a dotted line
y = (2x  6)/ (x25x+4)
i) Equation of any vertical asymptote(s)
ii) State any restrictions or nonpermissible value(s)
iii) Determine coordinates of any intercept(s)
iv) Describe the...
Homework Statement
$$\lim_{x\to\infty} \left(\frac{n^2+2n+1}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}$$
Homework Equations
3. The Attempt at a Solution [/B]
I tried
##\lim_{x\to\infty} \left(\frac{n^2+2n+32}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=##
##\lim_{x\to\infty}...
I am planning to selfteach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations.
Books:
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...
Homework Statement
Help i have a homework quiz done and i simply can't find out how to do the 3rd problem as we haven't even learned how to do it or maybe my notes aren't good or something , however I am close to an A in the class and this would help bring it closer. It asks me: "Find all the...
Homework Statement
Ok so this isn't really a problem, more like a problem set, I'm not sure if I'm able to understand it yet.
The context is determining all the primitive pythogrean triples
Letting x = a/c and y = b/c, we see that (x, y) is a point on the unit circle with rational number...
Homework Statement
http://imgur.com/a/Yq8pW
Homework Equations
projection u onto v: ((u x v)/(v^2)) x v
Unit vector: u/u
The Attempt at a Solution
For number 2, I absolutely do not know how to set up the problem. I do not know what vectors to use, I assumed F vector to be <0.00375...
Homework Statement
[/B]
Th value of 'a' for which the equation x3+ax+1=0 and x4+ax+1=0 have a common root is?
Homework Equations
The Attempt at a Solution
i initially thought of subtracting both the equations and then finding x and substituting back in the equation but it did not work.
.The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is
(1) 901 (2) 861 (3) 820 (4) 780
my attempt:
for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
I have repost this forum as I should have paid closer attention to rules. I apologized for that.
Homework Statement
1) The expression tan^3 θ + sinθ/cosθ is equal to:
(a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ
2) Simplify (cos θ/1+ sin θ  cosθ/sinθ1)^1...
[b[1. Homework Statement [/b]
##4^{3x}2^{4x+2}*3^{x+1}+20*12^x*3^x \ge 8*6^x(8^{x1}+6^x)##
The sets containing the real solutions for some numbers ##a, b, c, d,## such that ##\infty < a < b < c < d < +\infty## is of the form ##(\infty, a] \cup [b, c] \cup [d, +\infty)##. Prove it by...
Homework Statement
log(cosx)sinx = 4*log(sinx)cosx
Homework Equations
3. The Attempt at a Solution
i tried to solve it and uploaded my work but my last part reads
(cosx)^2 = sinx
(cosx)^(2) = sinx
its weird that i don't see where i have made a mistake[/B]
Homework Statement
The tangent line of a curve y=e^(x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin.
Homework Equations
Ar= xy/2
The Attempt at a Solution
Derivative of this function is y'=e^(x)
I took the formula of the...
Homework Statement
cos(x  3p/2) =  4/5
p <x< p/2
sin(x/2)*cos(5p/4)= ?
Homework Equations
The Attempt at a Solution
I made it as far as to determine that sinx= 4/5 and cosx =  3/5 but can't seems to progress any further. I am looking for an easier way to find the solution without having to...
Homework Statement
For clarification a have posted the equation below as a picture file.[/B]
Homework Equations
log(a*b)= loga + logb
log(a/b) = logalogb
log(a^n) = nloga[/B]
The Attempt at a Solution
I don't know how to start. I can't remember the rule for powering the logarithms if there...
Homework Statement
if x1 and x2 are solutions to 1) x² + x + 1 = 0, then 2) y1 = ax1 + x2 and 3) y2 = x1 + ax2 are solutions to which quadratic equation?
Homework Equations
ax² + bx + c = 0
x1∕2 = (−b ± √(b²  4ac))/2a
The Attempt at a Solution
Well, firstly i solved for x1 and x2 getting...
Hi everyone! I am starting to prepare for my admission test into college next year and I am looking for a best textbook which covers these topics ( with an adition of other it may also include but not disclude these)
Polynomials
Functions ( linear, quadratic )
Algebraic equations and...
Homework Statement and attempt at a solution[/B]
If 5 gifts are to be given among 8 children:
a) if the gifts are identical (indistinguishable) and no child can receive more than 1 gift, there are 8P5 ways
b) if the gifts are nonidentical (distinguishable) there are 5!(8P5) ways
In a), the...
Homework Statement
Homework Equations
The Attempt at a Solution
In order for me to figure out this problem I had to reverse the equality to isolate the Ө on the left side making the new equation 9cos(3Ө)=r^2. The first thing I’m going to do is change cos(3Ө) in terms of cos and sin. That...
What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too.
Elementary Algebra:
Gelfand's Algebra
Gelfand's Functions & Graphs
Burnside's Theory of Equations
Euler's Analysis of the...
What are some good textbooks, websites, question papers and other sources of information that will help me teach myself precalculus up to calculus? How long will this take until I have a good grasp of the knowledge?
Homework Statement
Determine a positive rational number whose square differs from 7 by less than 0.000001 (10^(6))
Homework Equations

The Attempt at a Solution
Let p/q be the required rational number.
So,
7> (p/q)^(2) > 7(0.000001)
⇒ √(7) > p/q > √(7.000001)
⇒√(7) q> p >...
Dear Physics Forum personnel,
I wrote this email because I am seeking a recommendation on selecting the precalculus textbooks. I have been studying the real analysis and number theory, and I felt that I need to brush up the algebra, functions, trigonometry, and geometry. So I decided to...
I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can...
Homework Statement
1 + 2 + 2^2 + 2^3 + ...+2^(n1) = 2^n  1
Homework Equations
Sum formula?
3. The Attempt at a Solution
I know you are suppose to use the base case and prove its true for k +1, but I'm not sure what to do for similar bases. Can someone please solve it step by step? Thanks!
https://www.amazon.com/dp/1133949010/?tag=pfamazon0120
https://www.amazon.com/dp/1285057090/?tag=pfamazon0120
https://www.amazon.com/dp/1133959741/?tag=pfamazon0120
So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...