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The distance s metres from a fixed point of a vehicle travelling in a straight line with constant acceleration, a m/s2, is given by s=ut + 1/2 at2, where u is the initial velocity in m/s and t the time in seconds. Determine the initial velocity and the acceleration given that s=42m when t =2 s and s=144m when t =4 s. Find also the distance travelled after 3 s
Use Gauss's law to find the charge enclosed by the cube with vertices {(+/-)1,(+/-)1,(+/-)1} if the electric field is E(x,y,z) = 4xi+2yj+1zk
Sam has a farm with 40 cows and chickens. Together they have 136 legs. How many chickens are on the farm?
a baseball diamond is a square 90 feet on each side. a player is running from home to first base at a rate of 15 feet per second. at what rate is his distance from second base changing when he has run halfway to first base?
The partners calculate that if they give the technician a raise of 8% and if they increase their own salaries by 5%, the gross annual salaries for all account personnel will rise from the current $1,086,000 to $1,156,500. What are the current annu..
Determine the mean oil production with 95 percent confidence
Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant.
Aaron looked through his closet and counted 33 shirts. He decided to sell some of them and with the money he earned, he bought 5 more shirts. He now counts that he has 15 shirts. How many shirts did Aaron sell?
What speed is the lamp's spot moving as it passes the point where it is perpendicular to shore? How fast is the spot moving along the shore when the spot is 1 km from the point at which it is perpendicular?
If the distance from point A to point B is greater than the distance from point B to Miami, then how far is it from point A to point B?
Seawater has density 1025 kg/m3 and flows in a velocity field v=yi+xj, where x ... where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of the flow outward through the hemisphere x2+y2+z2=9, z >0
find the maximum possible area of a trapezoid inscribed in a semicircle of radius 1.
A 2kg block sitting on a horizontal surface is subjected to a horizontal force of 7.5 N. If the resulting acceleration of the block is 3 m/s square, what is the magnitude of the friction force opposing the motion of the block?
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