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1. Consider the set of all continuous functions that satisfy the condition ƒ(0) = 0. Show that this is a vector space.
2. Show that the set of 2 × 2 matrices is a vector space.
Air flows into a convergent-divergent nozzle with an exit area 2.0 times the throat area of 0.005 m2. The inlet stagnation state is 1.2 MPa, 600 K. Find the back pressure that will cause a reversible supersonic exit flow with M = 1 at the throat. ..
Determine the minimum force P to prevent a 30kg rod AB from sliding on a wall. The contact surface at B is smooth, whereas the coefficient of static friction between the rod and the wall at A is Us=0.2.
What should be the mass m of the ram? Compute the velocity v of the pile immediately after impact if the ram is dropped from a height of 4 m onto the pile. Also compute the energy loss ?E due to impact at each blow.
Three streams of polluted air are combined prior to treatment in an electrostatic precipitator (ESP). The flow and particulate concentration of each stream are 600 cfm at150 mg/m^3, 700 cfm at 200 mg/m^3, and 500 cfm at 1000 mg/m^3.
a belt sander is being brought up to operating speed at the instant of the belt is rotating in the clockwise direction ar 4 ft/s and acceleration at 40 ft/s. the tensioning cylinders A and B have a radius of 2.5 in.
The storage in a rectangular section irrigation channel is 20,000 m2 at a given time. Determine the storage 1 hour later if the average rates of inflow and outflow during the hour are 23 and 18 m3/s respectively.
1 determine the design hourly volume for the road below recommend the k factor first.a. for a two lane highway in a
The length of the cord is 1050 mm, and the effects of the radius of the small pulley A may be neglected.
The grains of wood in the board make an angle of 20! with the horizontal as shown. Determine the normal and shear stress that act perpendicular and parallel to the grains if the board is subjected to an axial load of 250 N.
Water is flowing in a 6-cm diameter pipe at 20 m/s at 10?C. If the pipe enlarges to a diameter of 12-cm, calculate the reduced velocity. Also, calculate the mass flux rate and the flow rate.
A barge measures 10 ft (depth) by 35 ft by 120 ft and weighs 100 U.S. tons. The barge floats in fresh water (specific weight = 62.4 lb/ft3) and is evenly filled with 38,000 bushels of corn (60 lb/bushel).
The barrel has an inner diameter of 4ft. Neglect its wall thickness. Assume that only the hoops resist the water pressure. Note: Water develops pressure in the barrel according to Pascal's Law, p=62.4 lb/ft^2, where z is the depth from the surface..
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