If the derivative property of phasors is the multiplication of the phasor by jω, the integral property of phasors is division of the phasor by jω. Use phasors and these properties to find the sinusoids in each of the following:

(A) v2 (t) = (1/100) dvi(t)/dt + 20v1(t) and v1(t) = (a) vz(t) = 10 cos(100t + 90°) V
(B) i2(t) = 10 ∫[ i1(t)dt – 3i1(t)] and i1(t) = -4 cos(5t) A

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.

Consider a large isothermal enclosure that is maintained at a uniform temperature of 2000 k. calculate the emissive power of the radiation that emerges from a small aperture on the enclosure surface. what is the wavelength ? , below which 10% of the emission is concentrated? what is the wavelength ? 2 above which 10% of the emission is concentrated? determine the wavelength at which maximum spectral emissive power occurs. what is the irradiation incident on a small object placed inside the enclosure?

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.