Determine the cartesian coordinates of the points with polar coordinates (\sqrt{2}, \pi/4 ), (0, \pi), (-1,400\pi), and ( 2\sqrt{3},- 2\pi / 3)

Step-by-step explanation:

We have the conversion from polar coordinates to cartesian as

x =rcost and y = rsint where (r,t) are the polar coordinates

Also all trignometric functions are periodic with period = 2pi

Using this we find out

Thus we converted polar to rectangular coordinates.

Reverse would be

from (x,y) to (r,t) as

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1