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Probability Q : A die is thrown. A is the event that a prime number comes up, B is the event that a number divisible by three comes up, C is the event that a perfect square number comes up. Find the sample space S, find complementary events, mutually exclusive events.
A spring with a 2 kg mass attached to it has spring constant 8 N/m and no damping. There is an external force given by F(t) = 24 sin 2t N, where t is time. The mass is initially stretched 2 m beyond the equilibrium position and released with an in..
The tank shown below is full of water. Using the fact that the density of water is 1000kg/m3, find the work (in joules) required to pump the water out of the outlet.
The monthly sales at an import store are currently $10,000 but are expected to be declining at the rate of S'(t) = -10t^(2/5) dollars per month t months from now. The store is profitable as long as the sales level is above $8,000 per month. Find a fo..
Find the curvature of r→(t) = (t2, In t, t In t) at the point (1,0.0). A projectile is fired with an initial speed of 200 ni/s and angle of elevation is 60°. Find the range of the projectile. The maximum height reached.
Relative to polar coordinates, the position vector of an object moving in the plane can be written as r (t) = r(t)er. Verify that the velocity vector is v(t) = (dr/dt) er + r (dθ/dt)] eθ.
Suppose the position of a particle after t seconds is given by the following vector equation - evaluate each of the following vectors:
Poincare's model of Lobachevskian geometry was to say that points of the plane are represented by points in the interior of a circle and lines by both the diameters of the circle and the arcs of circles orthogonal to it. Draw a diagram(s) to illus..
but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done W in pulling the bucket to the top of the well.
A long, current-carrying solenoid with an air core has 1750 turns per meter of length and a radius of 0.0180 m. A coil of 125 turns is wrapped tightly around the outside of the solenoid. What is the mutual inductance of this system?
35% of a store's computers come from factory A and the remainder come from factory B.2% of computers from factory A are defective while 1% of computers from factory B are defective.
A random sample of 11 patients using the drug is selected. Find the probability that exactly two will have this mild side effect
Guy wires 80 feet long supporrt a 65-foot tall telephone pole. To the nearest degree, what angle will the wires make with the ground.
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