Question Friction: A \( 55-\mathrm{kg} \) box rests on a horizontal surface. The coefficient of static friction between the box and the surface is \( 0.30 \), and the coefficient of kinetic friction is \( 0.20 \). A horizontal push force is applied to the box and it starts moving. What must be the magnitude of the push to keep the box moving at a constant speed of \( 0.5 \mathrm{~m} / \mathrm{s} \) ? Express your answer with the appropriate units.

(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational (a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational angular momentum of the disk? What is the rotational kinetic energy of the disk? (Express your answer for rotational angular momentum in vector form.) Z rot = ! > kg.m /s Kot = (b) A sphere of uniform density, with mass 17 kg and radius 0.6 m, is located at the origin and rotates around an axis parallel with the x axis. If you stand somewhere on the +x axis and look toward the origin at the sphere, the sphere spins counterclockwise. One complete revolution takes 0.4 s. What is the rotational angular momentum of the sphere? What is the rotational kinetic energy of the sphere? (Express your answer for rotational angular momentum in vector form.) Z tot = < > kg-m /s Kot = (c) A cylindrical rod of uniform density is located with its center at the origin, and its axis along the z axis. Its radius is 0.04 m, its length is 0.7 m, and its mass is 5 kg. It makes one revolution every 0.09 s. If you stand on the +r axis and look toward the origin at the rod, the rod spins clockwise. What is the rotational angular momentum of the rod? What is the rotational kinetic energy of the rod? (Express your answer for rotational angular momentum in vector form.) > kg.m2/s Z rot = </ Kot =

Digital Signal Processing H.W.#1 COE463 Q#1: For each of the following difference equation determines: (a) Identify all coefficients ak and bk. (Hint: "a" for output and "b" for input) (b) Is this a recursive or non-recursive D.E. and why? (c) Draw the block diagram of each equation. (i) y[n] = 0.5y[n-1] + x[n] (ii) y[n] = x[n] – 0.3x[n-2] +0.7x[n-3] (iii) y[n] +0.5y[n-2] = 0.8x[n] +0.1x[n-1] – 0.3x[n-2] (iv) y[n] = 0.1x[n-2] -0.3y[n-2] +0.2x[n-1] -0.2y[n-1] + 0.8x[n] (v) y[n] – 0.4y[n-1] = x[n] – x[n-1]

This is a two-part question Consider the system of linear ODES de 41 (t) = 60 yy (t) – 16 y2 (+) + 77 73 (t). 92 (t) - 740 (t- 189 yą (t) +980 yz (t). dt 93 (t) = 96 y1 (t) - 24 32 (t) + 129 yg (t). (31(t) The system of equation written as y' (t) = Ay(t), where y(t) = 32(t) 33(t) (a) Enter the matrix A in the box below. ab sin(a) a f z 8 22 B 000 3 (b) Given that the matrix A has eigenvectors with respective eigenvalues 3.-4.1 Enter the solution of y(t) and yz(t) in Maple syntax, making sure the answer is consistent with the given form of y1 (t) 31(t) = 4A 43t+Be-4t-5 Cet y2(t) 33(t)

1. For a Solid Oxide Fuel Cell that uses hydrogen as fuel, calculate the maximum energy output possible at 800°C. 2. For a methanol fuel cell with total reaction equation and AG given, calculate the open circuit voltage. CH;OH + 3/2 O2 2H2O + CO2 AG = -698.2 kJ/mol 3. H2O is electrolyzed using an SOEC reactor. Inlet of the cathode has 30ml/min H20, outlet of anode has 5ml/min O2, and applied current is 2A. Calculate the H2O conversion and Faradaic efficiency (both in %). (Flow rates are given for gas phase in STP)

please help. with brief is possible. thank youwith 1 a, 1 b, 2 and 3 EXPERIMENTS Post-Laboratory Questions 1. In Step 24, you were instructed to wash the precipitates on the filter paper. a. Why was it necessary to wash the precipitate before drying. b. You were instructed to use dilute nitric acid to wash silver chloride, and to use distilled water to wash barium sulfate and calcium carbonate. Why was water used, in place of nitric acid, to wash barium sulfate and calcium carbonate? 2. Some precipitate is lost when the filter paper and precipitate is removed from the drying oven. The her paper and precipitate is subsequently weighed. Would the calculated percent by mass of the unknown lon in the compound be higher or lower than the true value? Justify your answer with an explanation 3. If the filter paper containing the precipitate is significantly charred in the drying oven because the oven temperature is to high, would the calculated percent by mass of the unknown lon in the compound be higher or lower than the true value? Justify your answer with an explanation

The probability density of a random variable $x$ is $$f(x)=a\ \cdotp x^2\ \cdotp \mathrm{e}^{−kx}\ (k>0,\ 0\leq x\leq \infty)$$ Then, the coefficient $a$ equals $$(i)\frac{k^3}{2}\ \ \ \ (ii)\ k^3 \ \ \ \ (iii)\ k^2 \ \ \ \ (iv)\ k \ \ \ \ (v) \frac{2\ \cdotp k}{\pi}$$ Here is what I've tried: $$\int_0^\infty f(x)\mathrm{d}x = 1$$ $$\int_0^\infty\left(a\ \cdotp x^2\ \cdotp \mathrm{e}^{−kx}\right)\mathrm{d}x = 1$$ solving by parts gives result as $$\left[-\frac{a\cdotp\mathrm{e}^{-kx}}{k}\cdotp\left(x^2+\frac{2x}{k}+\frac{2}{k^2}\right)\right]^\infty_0 = 1$$ Now, here I'm stuck. Can't find a way to solve $a$.