Recent content by adillhoff

Homework Statement Here you are supposed to perform system identification to determine the parameters required later to perform model compensation in your PD control loop. The dynamic model of this single joint manipulator has the form τ = Ia + Bv + G(x), where a is angular acceleration...

Homework Statement (a) The quadratic Chebyshev approximation of a function on [-1, 1] can be obtained by finding the coefficients of an arbitrary quadratic y = ax^2 + bx + c which fit the function exactly at the points (-sqrt(3)/2), 0, (sqrt(3)/2). Find the quadratic Chebyshev approximation of...

Wow that seems so obvious now. I completely overlooked it. Thank you so much for the help.

Homework Statement Define the function at a so as to make it continuous at a. f(x)=\frac{4-x}{2-\sqrt{x}}; a = 4 Homework Equations \lim_{x \rightarrow 4} \frac{4-x}{2-\sqrt{x}} The Attempt at a Solution I cannot think of how to manipulate the denominator to achieve f(4), so I...

Of course. I knew I missed something simple. Thanks for the reply.

Homework Statement Solve the compound interest formula for t by using natural logarithms. Homework Equations A=P(1+\frac{r}{n})^{nt} The Attempt at a Solution I start by dividing both sides by P. I then take the natural log of both sides and end up with ln(\frac{A}{P})=nt *...

Absolutely. Thank you so much for the help. I ended up with x=\frac{ln\frac{y+1}{y-1}}{20}

Homework Statement Use Natural Logarithms to solve for x in terms of y y = \frac{e^{10x}+e^{-10x}}{e^{10x}-e^{-10x}} Homework Equations I am not too sure. The Attempt at a Solution I multiplied both sides by the denominator first. Then I multiply by an LCD of e^{10x} I end up...

Yes that was a typo. I also mean to say that the midpoint of PQ = (-13/2, 1). I completely over-analyzed this problem as I do with many problems. I took your advice and found point R(-11, -23) by taking the difference between the x- and y-coordinates of P & Q. Thanks for your help!

Homework Statement Given P(-5, 9) and Q(-8, -7), find a point R such that Q is the midpoint of PR Homework Equations d = \sqrt{(x+8)^2+(y+7)^2} The Attempt at a Solution Because Q is the midpoint of PR, I know that d(P, Q) = d(Q, R). I also know that d(P, R) = d(Q, R), which is...

I wasn't quite sure if I could solve it that way, but it makes a lot of sense. After solving for a using the quadratic formula I get a = 1 - 2 and a = 1 + 2. The problem stated that the point is in the third quadrant which means a < 0. So I am left with a = 1 - 2 = -1. The answer ends up...

Homework Statement Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 5 from P(1, 3) Homework Equations \begin{distance} d(P_1, P_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{distance} The Attempt at a Solution To be quite...

That is a great reply. I've gotten a little further, but am stuck again. I used the Quadratic Formula to solve this and came up with y = (-1/m +- sqrt((1/m^2) - (4b - m))) / 2. I know that the problem has only one solution so sqrt((1/m^2) - (4b - m)) = 0. I am not sure what to do from this...

I do have the figure. It is simply a graph of x = y^2 and another line intersecting x = y^2 at (4, 2). I am given no other information on the line that is intersected x = y^2. I am instructed to find the slope of the line so that it only intersects x = y^2 at (4, 2). I have the answer to this...

Homework Statement Shown in the figure is the graph of x = y^2 and a line of slope m that passes through the point (4, 2). Find the value of m such that the line intersects the graph only at (4, 2) and interpret graphically.Homework Equations x = y^2 y = mx + bThe Attempt at a Solution Since...