Recent content by Cottontails

Homework Statement Two flat plates are oriented parallel above a fixed lower plate as shown below, The top plate, located a distance b above the fixed plate, is pulled along with speed V. The other thin plate is located a distance 0.3b (cb) above the fixed plate. This plate moves with speed...

I've recently done an experiment where I've obtained the strain of a channel section beam in bending. I used a strain gauge to get the strain from the midspan and also used dial gauges to get the deflections of the beam under different loading conditions. Along with the readings I've...

Homework Statement There is a vector space with set F, of all real functions. It has the usual operations of addition of functions and multiplication by scalars. You have to determine whether this equation is a subspace of F: f''(x) + 3f'(x) + x^2 f(x) = sin(x) Homework Equations f''(x) +...

So, you would convert that into a matrix to then solve for reduced row echelon form and as it is linearly independent, you should only have one value in each row, with the rest as zero. I have tried solving the matrix and obtained: \begin{pmatrix} 1 & 2 & 0 & | & 0\\ 0 & 1 & 2 & | & 0\\...

Sorry, I don't really understand by what you mean for having a separate row for each component? And how would you create it?

Okay, thanks. So I set up the matrix: \begin{pmatrix} 1 & 2 & 3 & 7 & 2 & 6 & | & 0 & 0\\ 1 & 0 & 0 & 0 & \alpha & 0 & | & 0 & 0 \end{pmatrix} I then did row operations and made the matrix into reduced row echelon form, obtaining: \begin{pmatrix} 1 & 0 & 0 & 0 & \alpha & 0 & | & 0...

Sorry, I didn't realize but I put the first entry as 3 instead of -3 and now I have corrected it. Is that correct now?

Homework Statement There is a vector space with real entries of all 2x2 matrices. You have to find what values of \alpha\inℝ make the set Z = \{ \begin{pmatrix} 1 & 2\\ 1 & 0 \end{pmatrix}, \begin{pmatrix} 3 & 7\\ 0 & 0 \end{pmatrix}, \begin{pmatrix} 2 & 6\\ \alpha & 0...

Homework Statement There is a vector space with real entries, in ℝ3 with the subset X = \begin{pmatrix} 2\\ -1\\ -3 \end{pmatrix}\\ , \begin{pmatrix} 4\\ 0\\ 1 \end{pmatrix}\\ , \begin{pmatrix} 0\\ 2\\ 7 \end{pmatrix} and you have to describe span(x) geometrically. Homework Equations In...

Homework Statement A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. Assume that the scoop of ice cream is a sphere with radius r = 3.65 cm that is placed into a 9.90 cm tall cone. The interior height of the cone is 9.00 cm. The cone...

Let f(x)=9-x^2. Let A be the area enclosed by the graph y=f(x) and the region y>=0. Suppose A is rotated around the vertical line x=7 to form a solid revolution S. So, using the shell method, I was able to find the indefinite integral used. I found the shell radius to be (7-x) and the shell...

Okay. Then, the parabola opens upward, with the y-intercept at (0,3). It has no x-intercepts but the opening (with how it expands/terms of width) of the curve is within x=-4, x =4. Yes, I realized that my x-intercepts are wrong. The x-intercepts are √3 and -√3, right? So, should I draw...

Oh, wow. Thanks for pointing that out!

Homework Statement Find the 6th complex roots of √3 + i. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution When k=0, z = 2^1/6(cos(π/36)+isin(π/36)), When k=1, z = 2^1/6(cos(13π/36)+isin(13π/36)), When k=2, z =...

Okay, thanks. Moreover, is this correct for part (a)?