In a test for a Springfield rifle, a bullet of 9.7 g hits a block of wood of 3 kg. The block of wood is held by pendulum of length 1.5 m and the angle with respect to the vertical where the velocity goes to zero is 64 degrees. What is the speed of the bullet before impact? Assume the acceleration due to gravity to be 9.8 m/s 2 . Also assume that the mass of the bullet is negligible compared to the mass of the block. Answer in units of m/s.

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