Aroman centurion fires off a vat of burning pitch from
hiscatapult at 18.2m/s, 37 degrees above the horizontal.
a. how long was the vat in the air?
b. determine the horizontal component of the initial
velocityof the vat.
c. determine the range of the vat.

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