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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)