Given points (r1, u1 ) and (r2, u2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 u 1 sin2 u 5 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula.

Step-by-step explanation:

The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1

(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