A merry-go-round at an amusement park is initially at rest. It begins to rotate at time t = 0 . The angle through which it rotates is defined by θ(t) = ( t + ke−t/k) , where k is a positive constant, t is in seconds, and θ is in radians. Find the angular velocity of the merry-go-round at t = T.

Which are examples of projectile motion? choose all that apply a. a soccer ball rolling across the ground in the northeast direction b. a car turning a corner, so it is heading south c. a javelin flying through the air d. a tennis ball lobbed over the net

In a heat engine if 1000 j of heat enters the system and the piston does 500j of work, what is the final internal energy of the system if the inital energy was 2000 j1.write the equation2.list out your known variables 3. plug the numbers into the equations4.solve 5.write your solution statement that includes initial energy and final energy added.

For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. u with bar on top space equals space x to the power of 1 third end exponent z to the power of 2 over 3 end exponent suppose initial values for income and the prices of goods x and z are y equals 90, p subscript x equals space 10, and p subscript z equals 15 respectively, then the price of good x falls to syntax error from line 1 column 89 to line 1 column 100. unexpected '\'.. what is the magnitude of the total effect