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1.Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h^2) to estimate the first derivative of the function examined in prob. 4.5. evaluate the derivative at x=2 using a step size of h=0.2. compare your results with the true value of the derivative. interpret your results on the basis of the remainder term of the taylor series expansion.
2.We know that the molar concentration and volume of a solution is the sum of the product of the molar concentration and volume of each solution component before mixing: M1V1 = M2V2 + M3V3. Using the information below, calculate the final molar concentration of the mixture (M1) with units of mol/mL. (Watch the units) M2=0.60 mol/L V2=6 mL M3=0.15 mol/L V3=10 mL
A sailor is being rescued using a boatswain's chair that issuspended from a pulley that can roll freely on the support cableACB amd is pulled at a constant speed by cablle CD
Airplane tows a 2m tall advertising banner at a speed of 160 Km/hr. If the banner is flat and 5m long, then estimate its drag assuming fully turbulent flow.
a mechanic uses a crowfoot wrench to loosen a bolt at c. the mechanic holds the socket wrench handle at points a and b
Calculate the largest tolerable internal crack length for a 7075-T651 aluminum alloy component that is loaded to a stress one-half of its yield strength without catastrophic fracture. For the alloy, the plane strain fracture toughness is 24 and yi..
Solve the following initial value problem over the interval from t=0 to 2 where y(0)=1 a. Euler method with step h=0.5 b. Midpoint method with h= 0.5
The direct strain at an angle of 30o,to one of theprincipal axes was 1.34x10-3 and the corresponding shearstrain was 8.52x10-4. Calculate as many principal or maximum strains at the point
Tabulate station elevations for a 200-ft equal-tangent parabolic curve with g1= -1.25%, g2= +1.25%, VPI station = 146+00, and VPI elevation = 1,895.00 ft. Compute values if stakeout is at 30-ft increments. Check by second differences
The two shafts are made of A-36 steel. Each has a diameter of 25 mm and they are connected using the gears fixed to their ends. Their other ends are attached to fixed supports at A and B.
Consider tetrachloroethene (PCE) in water. The vapor pressure of PCE is 0.0251atm. Henry's constant for PCE at 25°C is 26.9 atm-L/mol. Estimate the aqueous concentration of PCE in water at equilibrium
What would be the load carrying capacity of a 250 mm-diameter and 15 m-long timber pile driven into soft clay with an unconfined compressive strength of 40 Kpa? What percentage of the total load is carried by the shaft?
A biological reactor is used to treat wastewater from a small community (Q = 100,000 gpd). The influent BOD5 concentration to the reactor is 200 mg/L and the required effluent BOD5 concentration is 30 mg/L.
What is the percent change in pressure that a scuba diver in salt water will feel going from 50 to 40m of depth? What is the percent change from 10m to the surface? Use absolute pressure and assume standard atmospheric conditions. Would the answer ch..
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