Recall the differential equation for the instantaneous charge q (t) on the capacitor in an LRC series circuit is given by L d^2 q/dt^2 + R dq/dt + 1/C q = E(t). Use the Laplace transform to find q(t) when L = 1 henry, R = 20 ohms, C = 0.005 farads, E(t) = 50 volts, t > 0, q (0) = 0, and i (0) = 0. What is the current i(t)?

its a straight line parallel to the time axis

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week