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Using Newton's method with initial guess x0 = 2 for f(x) = x^2 - 5, what is the next approximation x1?
Answer · A
Newton's method: x1 = x0 - f(x0)/f'(x0). f(2) = 4 - 5 = -1. f'(2) = 4. x1 = 2 - (-1)/4 = 2.25.
For a standard normal distribution, approximately what percentage of data falls within +/-1 standard deviation of the mean?
Answer · A
The empirical rule is 68-95-99.7: about 68% lies within one standard deviation of the mean.
According to the NSPE Code of Ethics, engineers shall hold paramount:
Answer · B
The fundamental canon of engineering ethics is that engineers shall hold paramount the safety, health, and welfare of the public.
What is the present worth of $10,000 to be received 3 years from now at i = 8%?
Answer · A
P = F/(1+i)^n = 10,000/(1.08)^3 = $7,938.
A 12 V battery is connected to a 4 ohm resistor. What is the current flowing through the circuit?
Answer · A
Ohm's law: I = V/R = 12/4 = 3 A.
Using the support reaction labels shown, what is the ratio of the reaction at A to the reaction at B?
Answer · A
The figure labels show the reaction at A is 7.33 kip and the reaction at B is 4.67 kip. Therefore the requested ratio is 7.33 / 4.67 = 1.57.
A car accelerates from rest at 3 m/s^2 for 5 seconds. What is the final velocity?
Answer · A
v = v0 + at = 0 + 3(5) = 15 m/s.
A steel rod with diameter 20 mm is subjected to a 50 kN tensile load. What is the normal stress?
Answer · A
A = pi(20)^2/4 = 314.16 mm^2. Stress = P/A = 50,000/314.16 = 159.2 MPa.
A material has yield strength 250 MPa. Under an applied stress of 125 MPa, the factor of safety against yielding is:
Answer · A
Factor of safety = yield strength / applied stress = 250/125 = 2.0.
Ignoring weight, what is the magnitude of the horizontal force F for the pipe-bend flow shown, most nearly?
Answer · C
Continuity gives ṁ = ρA₁V₁ = 1,000 x 0.2 x 5 = 1,000 kg/s. In the x-direction, P₁A₁ - P₂A₂cos(θ) - F = ṁ(V₂cos(θ) - V₁), so F = 4,608 N, which rounds to 4,610 N.
A container holds 2 moles of ideal gas at 300 K and 100 kPa. What is the volume? (R = 8.314 J/(mol*K))
Answer · A
PV = nRT. V = nRT/P = 2(8.314)(300)/100,000 = 0.0499 m^3.
Drag the terms to their correct positions on the plane-wall diagram so the heat transfer rate is positive in the indicated direction, based on Fourier's law as shown. Which placement is correct?
Answer · D
With heat transfer positive to the right and Q̇ = -kA(T₂ - T₁)/L, the upstream left surface is T₁ and the downstream right surface is T₂. The material property inside the wall is k, and the distance between wall faces is L.
A thermocouple has accuracy +/-1.2 C and a data logger has accuracy +/-0.5 C. The combined uncertainty by RSS is:
Answer · A
RSS method: u = sqrt(1.2^2 + 0.5^2) = sqrt(1.69) = 1.3 C.
A thin-walled cylindrical pressure vessel has P = 2 MPa, r = 500 mm, and t = 10 mm. What is the hoop stress?
Answer · A
Hoop stress for a thin-walled cylinder is sigma_h = Pr/t = 2(500)/10 = 100 MPa.
Using the belt tensions and pulley diameter shown, what torque is applied to the pulley by the belt?
Answer · B
The torque is the belt tension difference times pulley radius: (1280 - 500) N x 0.2 m = 156 N*m.
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