The polar coordinates of a certain point are (r = 2.75 cm, θ = 219°). (a) find its cartesian coordinates x and y. x = cm y = cm (b) find the polar coordinates of the points with cartesian coordinates (−x, y). r = cm θ = ° (c) find the polar coordinates of the points with cartesian coordinates (−2x, −2y). r = cm θ = ° (d) find the polar coordinates of the points with cartesian coordinates (3x, −3y). r = cm θ = °

(a) x = 2.14 cm and y = 1.73 cm ⇒ the point is (-2.14 , -1.73)

(b) r = 2.75 cm, Ф = 321.05°

(c) r = 5.50 cm, Ф = 38.95

(d) r = 8.26 cm, Ф = 141.05°

Step-by-step explanation:

* Lets explain the relation between the polar coordinates and the

  Cartesian coordinates

- The polar coordinates are (r , Ф°)

- The Cartesian coordinates are (x , y)

- and Ф =

- x = r cosФ

- y = r sinФ

* Lets solve the problem

- The polar form of the point is (r = 2.75 cm, θ = 219°)

(a)

∵ r = 2.75 cm and Ф = 219°

∵ x = r cosФ and y = r sinФ

∴ x = 2.75 (cos 219) = -2.14

∴ y = 2.75 (sin 219) = -1.73

- The point (x , y) lies on the 3rd quadrant

∴ x = 2.14 cm and y = 1.73 cm

- We neglect (-) in the answer only because no negative values for cm

(b)

- We want to find the polar coordinates of (-x , y)

- That means we want to find the polar coordinates of (2.14 , -1.73)

∵ This points lies on the 4th quadrant

∴ Ф will lies between 270° and 360°

∵

∴

∴ r = 2.75

∵ α = , where α is acute angle

∵ Ф lies in the 4th quadrant, then Ф = 360° - α

∴ Ф = 360 - 38.95 = 321.05°

∴ r = 2.75 cm, Ф = 321.05°

(c)

- We want to find the polar coordinates of (-2x , -2y)

- That means we want to find the polar coordinates of (4.28 , 3.46)

∵ This points lies on the 1nd quadrant

∴ Ф will lies between 0° and 90°

∵

∴

∴ r = 5.50

∵ α = , where α is acute angle

∵ Ф lies in the 1st quadrant, then Ф = α

∴ Ф = 38.95

∴ r = 5.50 cm, Ф = 38.95

(d)

- We want to find the polar coordinates of (3x , -3y)

- That means we want to find the polar coordinates of (-6.42 , 5.19)

∵ This points lies on the 2nd quadrant

∴ Ф will lies between 90° and 180°

∵

∴

∴ r = 8.26

∵ α = , where α is acute angle

∵ Ф lies in the 2nd quadrant, then Ф = 180° - α

∴ Ф = 180 - 38.95 = 141.05°

∴ r = 8.26 cm, Ф = 141.05°

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

i don't have the answer rn but go to math papa. it shows the steps and the answer. hope this : )

step-by-step explanation: