Chapter 11, Problem 92CP

8. In the following check to see if the set S is a vector subspace of the corresponding Rn. If it is not, explain why not. If it is, then find a basis and the dimension. X1 (a) S = X2 {[2], n ≤ n } c X1 X2 CR² X1 (b) S X2 = X3 X4 x1 + x2 x3 = 0

2) Suppose that two unequal masses m₁ and m₂ are moving with initial velocities V₁ and V₂, respectively. The masses hit each other and have a coefficient of restitution e. After the impact, mass 1 and 2 head to their respective gaps at angles a and ẞ, respectively. Derive expressions for each of the angles in terms of the initial velocities and the coefficient of restitution. m1 m2 8 m1 ↑ บา m2 ñ В

The fallowing question is from a reeds book on applied heat i am studying. Although the answer is provided, im struggling to understand the whole answer and the formulas and the steps theyre using. Also where some ov the values such as Hg and Hf come from in part i for example. Please explain step per step in detail thanks   In an NH, refrigerator, the ammonia leaves the evaporatorand enters the cornpressor as dry saturated vapour at 2.68 bar,it leaves the compressor and enters the condenser at 8.57 bar with50" of superheat. it is condensed at constant pressure and leavesthe condenser as saturated liquid. If the rate of flow of the refrigerantthrough the circuit is 0.45 kglmin calculate (i) the compressorpower, (ii) the heat rejected to the condenser cooling water in kJ/s,an (iii) the refrigerating effect in kJ/s. From tables page 12, NH,:2.68 bar, hg= 1430.58.57 bar, hf = 275.1 h supht 50" = 1597.2Mass flow of refrigerant--- - - 0.0075 kgls 60Enthalpy gain per kg of refrigerant in…

state the formulas for calculating work done by gas

Exercises Find the solution of the following Differential Equations 1) y" + y = 3x² 3) "+2y+3y=27x 5) y"+y=6sin(x) 7) y"+4y+4y = 18 cosh(x) 9) (4)-5y"+4y = 10 cos(x) 11) y"+y=x²+x 13) y"-2y+y=e* 15) y+2y"-y'-2y=1-4x³ 2) y"+2y' + y = x² 4) "+y=-30 sin(4x) 6) y"+4y+3y=sin(x)+2 cos(x) 8) y"-2y+2y= 2e* cos(x) 10) y+y-2y=3e* 12) y"-y=e* 14) y"+y+y=x+4x³ +12x² 16) y"-2y+2y=2e* cos(x)

The state of stress at a point is σ = -4.00 kpsi, σy = 16.00 kpsi, σ = -14.00 kpsi, Try = 11.00 kpsi, Tyz = 8.000 kpsi, and T = -14.00 kpsi. Determine the principal stresses. The principal normal stress σ₁ is determined to be [ The principal normal stress σ2 is determined to be [ The principal normal stress σ3 is determined to be kpsi. kpsi. The principal shear stress 71/2 is determined to be [ The principal shear stress 7½ is determined to be [ The principal shear stress T₁/, is determined to be [ kpsi. kpsi. kpsi. kpsi.

Repeat Problem 28, except using a shaft that is rotatingand transmitting a torque of 150 N * m from the left bearing to the middle of the shaft. Also, there is a profile keyseat at the middle under the load.      (I want to understand this problem)

Prob 2. The material distorts into the dashed position shown. Determine the average normal strains &x, Ey and the shear strain Yxy at A, and the average normal strain along line BE. 50 mm B 200 mm 15 mm 30 mm D ΕΙ 50 mm x A 150 mm F

Prob 3. The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the shear strain, Yxy, at A. Prob 4. The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the average normal strain & along the x axis. Prob 5. The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the average normal strain &x along the x' axis. x' 45° 800 mm 45° 45% 800 mm 5 mm