What is the partial fraction decomposition of
7x squared- 6x +9/
3x(4x squared +9)

9514 1404 393

  1/(3x) =(x -2)/(4x^2 +9)

Step-by-step explanation:

The denominator cannot be factored further, so the final form will be ...

  A/(3x) + (Bx +C)/(4x^2 +9)

The value of this is ...

  (A(4x^2 +9) +(3x)(Bx +C))/(3x(4x^2 +9))

  = ((3B+4A)x^2 +3Cx +9A)/(3x(4x^2 +9))

Equating coefficients gives ...

  3B+4A = 7

  3C = -6   ⇒   C = -2

  9A = 9   ⇒   A = 1

Using the found value of A, we find ...

  3B +4 = 7   ⇒   B = 1

Then the decomposition is ...

(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