What is the exact value of Cosine (StartFraction 11 pi Over 21 EndFraction) cosine (StartFraction pi Over 7 EndFraction) minus sine (StartFraction 11 pi Over 21 EndFraction) sine (StartFraction pi over 7 EndFraction)? Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Negative one-half
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Option (2)

Step-by-step explanation:

Given trigonometric expression is,

This expression is in the form of an identity,

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

By substituting the values of A = and B = in the identity,

= cos

                                                  = cos

                                                  = cos

                                                  = cos

                                                  = -

Therefore, Option (2) will be the answer.

no solution

step-by-step explanation:

there is not enough information in the problem to solve.

(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