(a) Find Cartesian coordinates for the polar point (-1, -1) and plot the point. (b) Find Polar coordinates with r > 0 and -1 < <a for the Cartesian point (-1, V3) and plot the point. (c) Convert the equation x2 + y2 = x to polar form and sketch the curve. (d) Convert the equation r = 5 csc @ to Cartesian form and sketch the curve.
1 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi for a. r> 0 and 0 << 271 p < 0 and 0 < < 271 )
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
Find the length of spiral curve T() = ----- 0 < > < 2”
pls show the work clearly 9. Find | V x F ñds where F =< 22,4x, 3y >, the surface S is the cap of the sphere S x2 + y2 + z2 = 169 above xy-plane and the boundary curve C is the boundary of S.
Use induction to prove that 0–0 4j3 = n4 + 2n3 + n2 where n > 0.
Q.8. Balance the following equation. _Co (NO3)2 (aq) +_(NH4)2S(aq) => _Co2S3() + _NH4NO3(aq)
How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
Find the rectangular coordinates for the point whose polar coordinates are given. 8 TT 6 (x, y) = ) =( Convert the rectangular coordinates to polar coordinates with r> 0 and 0 se<2n. (-2, 2) (r, 0) Convert the rectangular coordinates to polar coordinates with r> 0 and O So<211. (V18, V18) (r, ) = Find the rectangular coordinates for the point whose polar coordinates are given. (417, - ) (x, y) =