Write the polar equation in rectangular form. r = 6 sin θ

y = –6x

y = x – 3

x2 + (y – 3)2 = 9

(x – 3)2 + y2 = 9

The rectangular form of the polar equation is x² + (y - 3)² = 9 ⇒ 3rd answer

Step-by-step explanation:

The graph of the polar equation r = a sin Ф is a circle where

∵ The polar equation is r = 6 sin Ф

- That means the graph of the equation is a circle

∴ The polar equation represents a circle

∵ a = 6

∵ The coordinates of the center of the circle are (0 , a/2)

∵ 6 ÷ 2 = 3

∴ The coordinates of the center of the circle are (0 , 3)

∵ The coordinates of the center of the circle are (h , k)

∴ h = 0 and k = 3

∵ The length of the diameter of the circle = a

∴ The length of the diameter of the circle = 6

- The length of the radius of the circle is half to the length

    of the diameter

∴ The length of the radius = × 6 = 3

∴ r = 3

- Substitute the values of h, k and r in the rectangular form of

   the equation of the circle

∵ (x - 0)² + (y - 3)² = (3)²

∴ x² + (y - 3)² = 9

The rectangular form of the polar equation is x² + (y - 3)² = 9

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

days of the week

step-by-step explanation:

javier earned more money then kyle, so that won't always be a constant term, but the days of the week do not change so that term is always constant.

edit: i meant