To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem. This problem introduces Kirchhoff's two rules for circuits: Kirchhoff's loop rule: The sum of the voltage changes across the circuit elements forming any closed loop is

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