Find the area bounded by the graphs of

  (9ln(3) -6)/4 ≈ 0.97187765

Step-by-step explanation:

A horizontal slice of the area will range from g^-1(y) to f^-1(y). The inverse functions are ...

  f^-1(x) = 1/2·ln(x)

  g^-1(x) = -1/4·ln(x)

Then the integral can be written as ...

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The attachment shows a numerical integration using a vertical slice of area. The result is identical to 12 significant figures.

(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