Use green's theorem to compute the area inside the ellipse( x^2/13^2)+(y^2/6^2)=1.
use the fact that the area can be written as

dub intd dxdy=(1/2) int partiald (-y dx+x dy) .
hint: x(t)=13cos(t).
the area is?

b)
find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the interior.
hint: x(t)=8cos^3(t).

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

Lizette is training for a marathon. at 7: 00 she left her house and ran until 8: 30, then she walked until 11: 30. she covered a total distance of 18 miles. her running speed was six miles per hour faster than her walking speed. find her running and walking speeds in miles per hour.

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?