Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t increases. x = t + sin(t), y = cos(t), −π ≤ t ≤ π

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

differentiating equation (1)  with respective to 'x'

differentiating equation (2)  with respective to 'y'

The length of curve is

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

again using formula, 1+cost = 2cos^2(t/2)

Taking common we get ,

length of curve =

length of the curve is = 4(1+1) = 8

conclusion:-

The arrow of the direction or the length of curve = 8

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.