The angle θ=π3 is in standard position and has a terminal side that coincides with the graph of a proportional relationship represented by y=kx.

a. Find the constant of proportionality, k.

b. Write an ordered pair that lies on the graph of y=kx.

Part a

theta = pi/3

sin(pi/3) = sqrt(3)/2

cos(pi/3) = 1/3

tan(angle) = opposite/adjacent = rise/run = slope

tan(pi/3) = sin(pi/3)/cos(pi/3) = (sqrt(3)/2)/(1/2) = sqrt(3)

This is also the slope the line y = kx because it is in the form y = mx+b with m = sqrt(3) and b = 0.

Part b

Pick any value you want for x, and plug it in to find the paired value of y

if x = 0, then y = 0 because

y = sqrt(3)*x = sqrt(3)*0 = 0

If x = 1, then y = sqrt(3), since,

y = sqrt(3)*x = sqrt(3)*1 = sqrt(3)

If x = sqrt(3), then,

y = sqrt(3)*x = sqrt(3)*sqrt(3) = sqrt(3*3) = sqrt(9) = 3

2.56 is the width of the garden

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