let s = 100/(t2+12) be the position function of a particle moving along a coordinate line, where s is in feet and t is in seconds. (a) find the maximum speed of the particle for t 0. if appropriate, leave your answer in radical form.

Step-by-step explanation:

Let's remember we could write the speed as a function of position taking the derivative whit respect to time.

Now, evaluating the speed at t₀, we have:

It would be the maximun speed at that time.

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step-by-step explanation:

(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