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:
$$2r^{2}+2\tau^{2}-1-\tau^{2}r^{2}=2\tau\left[2-r\right]\cos\varphi$$
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 x-axis, 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=2x-3 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 one-to-one function such that f(-3)=5 , find x given that f^-1 (5)=3x-1.
Here's how I attempted to solve the problem:
-3=3x-1
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)/ (x2-5x+4)
i) Equation of any vertical asymptote(s)
ii) State any restrictions or non-permissible 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+3-2}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=##
##\lim_{x\to\infty}...
I am planning to self-teach 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 im 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 co-ordinates 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 re-post 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/sinθ-1)^-1...
[b[1. Homework Statement [/b]
##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| \ge 8*6^x(8^{x-1}+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 dont 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 cant seems to progress any further. Im 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) = loga-logb
log(a^n) = nloga[/B]
The Attempt at a Solution
I dont know how to start. I cant 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 im 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 inequalities...
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 non-identical (distinguishable) there are 5!(8P5) ways
In a), the...