a few useful properties of fourier transforms a) proove parseval's theorem (10) for any regular function g(k) exp(ikr)dk with f(x) exp(-ikx)dr b) the convolution of two functions fi and f2 is defined as the integral show that if g(k) is the fourier transform of f(x) and gi(k) and g2(k) are the fourier transforms of fı(x) and f2(x) respectively, then

The heater element of a 120 v toaster is a 5.4 m length of nichrome wire, whose diameter is 0.48 mm. the resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 ω·m. the toaster is operated at a voltage of 120 v. (a) what is the power drawn by the toaster? (b) if the cost of electricity is 12 ¢ per kilowatt-hour, and it takes 2 minutes to toast bread, how much does it cost for toasted bread? (c) when the heater element is at room temperature, is the resistivity in the nichrome wire greater than, less than, or equal to it’s resistivity when at operating temperature? explain.