Recent content by Sociomath

1. Show that T isn't a linear transformation and provide a suitable counterexample. ##T \begin{bmatrix}x\\y \end{bmatrix} = \begin{bmatrix}x - 1 \\ y + 1 \end{bmatrix}## 2. The attempt at a solution ##\text{let}\, \vec{v} = \begin{bmatrix}0\\0 \end{bmatrix}. \text{Then,}## ##T(\vec{v}) =...

##\left[T_{a}\right]\left[T_{b}\right] = \begin{bmatrix}-1 & -1 \\ 2 & 0 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}-x -y\\ 2x \end{bmatrix}##

Am I on the right path here? 1. Homework Statement i. Prove that ##T_{a}## and ##T_{b}## are linear transformations. ii. Compose the two linear transformations and show the matrix that represents that composition. 2. The attempt at a solution i. Prove that ##T_{a}## and ##T_{b}## are linear...

Thanks, PeroK. How far along the beam can a man of weight 70 kg walk without the cable breaking? ##\displaystyle \tau_{pivot} = \tau_{cw} - \tau_{ccw}## d = 4 m = length of beam ##0 = Fgm(\frac12 \cdot 4m) \sin 37° + Fgm(x \cdot 4m) \sin 37° - F_{wall} (4m) \sin 53°## ##F_{wall} (4m) \sin 53°...

Hi, I need some guidance on the following problem, please. A daredevil attempts to walk the full length of suspended. A 20 kg wrecking ball hangs at the end of this uniform beam of length 4 m and mass 10 kg and is attached to a hinged wall at an angle of 53 degrees. A cable attached to the wall...

Are these correct? Thanks in advance! 1.) Set up the triple integral for ##f(x,y,z) = xy + 2xz## on the region ##0 ≤ x ≤4, 0 ≤ y ≤ 2## and ##0 ≤ x ≤ 3xy + 1##. ##\displaystyle \int_0^4 \int_0^2 \int_0^{3xy+1} 2y +2xz\ dz\ dy\ dx## \text{2.) Set up the triple integral in cylindrical...

Checking my steps and answer. Thanks in advance! Compute \int_0^3 \int_0^2 \int_1^3 xyz\ dz\ dy\ dx. \int_0^3 \int_0^2 \frac{xyz^2}{2} \Big|_1^3 = \frac{9xy}{2}-\frac{xy}{2} = \frac{8xy}{2} = 4xy \int_0^3 2xy^2 \Big|_0^2 \int_0^3 8x\ 4x^2 \Big|_0^3 = 36

Thanks LCKurtz and az_lender! 1. ##\displaystyle \int_2^4 \left(3-\left(5-x\right)\right)dx\,+\,\displaystyle \int_4^6\left(\left(3-\left(x-3\right)\right)\right)dx## :: :: 2. ##\displaystyle \int_1^3 ((y+3-(5-y))dy\,=\,\int_1^3 (2y-2))dy## :: :: 3. Using (1.) from above: ##\displaystyle...

Hi, I just need these solutions checked. Thank you in advance! Consider the region bounded by the following curves ##y=x-3, y=5-x, \text{and}\ y=3##: 1.) set up an integral expression that would give the area of the region of y as a function of x: ##y = x-3 = 5-x## ##x + x - 3 -...