Calculate the fourier series integrals by hand ie no

Question

1. A certain electric current is pulsating so that the current as a function of time is given by

Find the constant term, a₀, the first four cosine terms, and the first four sine terms of the Fourier series for this pulsating current. Calculate the Fourier series integrals by hand (i.e., no calculator or computer computation of the Fourier series for this problem). Use the integral table as needed. Use Desmos to graph three periods of the function f(t) and the Fourier series you found. Print out your graph to turn in.

2. According to Newton's Law of Cooling, the rate at which a body cools is proportional to the difference in temperature between it and the surrounding medium. An object whose temperature is 100 °C is placed in a medium whose temperature is 20 °C. The temperature of the object falls to 50 °C in 10 minutes. Assuming Newton's Law of Cooling applies, express the temperature, T, of the object as a function of time t (in minutes).

Answer 1

By applying the Newton's Law, solve the numerical problem and find out the result. Please show your work. According to the Newton's Law of Cooling, the rate at which a body cools is proportional to the difference in temperature between it and the nearby medium. The object whose temperature is 100 °C is put in a medium whose temperature is 20 °C. The temperature of the object drops to 50 °C in 10 minutes. Supposing Newton's Law of Cooling applies, state the temperature, T, of the object as the function of time t (in minutes).