Recent content by johnstobbart

Ray, I completely forgot about being able to check questions like these. I want to sincerely thank you for reminding me of this rule.

Hello everyone, I have a linear algebra question regarding Cramer's rule. Homework Statement Using Cramer's rule, solve for x' and y' in terms of x and y. \begin{cases} x = x' cos \theta - y' sin \theta\\ y = x' sin \theta + y'cos \theta \end{cases} 2. Homework Equations ##sin^2 \theta...

Thanks for the reply HallsofIvy. That explains why ∅ is a subset of {{∅}}, while {∅} is not. ∅ is a subset of every set, while {∅} is not because that it is the set that contains only ∅. Is that correct?

Homework Statement Hello. Here is the question: Determine whether or not R is some sort of order relation on the given set X. X = {∅, {∅}, {{∅}} } and R ε ⊆. I can't seem to figure out why the ordered pairs given are what they are. Homework Equations None. The Attempt at...

Thanks a lot, JesseC, dydxforsn and Ray Vickson. I really appreciate the time and effort you took to help me solve this problem. These forums are a huge help. Thanks a lot!

Sorry for not using pencil and paper, but I thought a graph program would suffice. I got -3 because you said a gradient of 1 = 45°. 45 * 3 = 135°. I input y = 3x on the graph, which didn't seem to be 135°, so to get it in the next quadrant, I put in -3x to get a line that looked as though it was...

OK. I've drawn a line f(x) = -3x, which is 135 degrees to the x-axis using a graphing program. I think I have it now. Now that I have the gradient, all I need to do is find the derivative of f(x), which is - 2sin x cos x. Then I make f '(x) = 3, and that should give my x value, right? Then how...

I did misunderstand. If that's the case, would the gradient be -√2/2?

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, ~x~\epsilon~[0, \frac{\pi}{2}] which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along...

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, x \epsilon [0, \frac{\pi}{2} which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along the...

I haven't started on integration yet, but I do know I'll be doing it soon. Thanks a lot for all your patience and time Millenial and Ray Vickson.

Sorry. I made an error. Let me try fix it. When I simplify f(x) (hopefully correctly this time), I get: \begin{equation} x^{1/2} - 3x \end{equation} Then when taking the derivative, I get: \begin{equation} \frac{x^{-1/2}}{2} - 3 \end{equation} My final answer is: \begin{equation}...

Homework Statement I have a bit of confusion surrounding one of my basic derivative problems: Find the derivative of the following: \begin{equation} f(x) = \frac{x - 3x{\sqrt{x}}}{\sqrt{x}} \end{equation} Homework Equations None, I believe. The Attempt at a Solution I...

Yes, I did mean cos (x) = 0 whenever x = ... I see it now. Trig has never been my strong point and I'll make sure to practise it some more, especially the basics. Thanks a whole lot for being so patient Mentallic and ehild.

Yes, I did mean cos (x) = 0 whenever x = ... I see it now. Trig has never been my strong point and I'll make sure to practise it some more, especially the basics. Thanks a whole lot for being so patient Mentallic and ehild.