The height of a rocket, launched from the ground, is given by the function y = 30 t − 5 t 2 , where y is in meters and t is in seconds. An observer is sitting at ground level a distance d from the launch point. If r is the distance between the observer and where the rocket is, show that dr/dt = ( 30 t − 5 t 2 ) ( 30 − 10 t )/ √ ( 30 t − 5 t 2 ) 2 + d 2 . Show all your work.

22

step-by-step explanation:

22

(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

13664

step-by-step explanation:

=cross multiply

=100 x = 13664