Question

Need help with problems 1) b) ii), 2) b) and c), and 3) c) please!

MAT All about Given a general line y mx + b, convert to polar coordinates and solve for r. Check your answer with Desmos (add sliders for b, m). 1) a) rG b-mccre)- r -mces =Fcese, y=rtnb rsin6= mreese +h int-mr b Assume m<0 so that the line, the y-axis, and x-axis enclose a triangular area: b) Area e Xheigh) Use geometry to determine a general expression for the area of this triangle (in terms of m and b) i) 2m A= 2m Set up an integral in polar coordinates that would give that area to integrate. and use Maple 14 Given the following right-triangular region: 2) Write the equation of the vertical line xb in polar coordinates and solve for r. a) The region covers angles from 0 to (??), give an expression for this maximum angle in b) rms of b and h. 6rceso Set up an integral using polar coordinates for the area of the region and compute it c) manually. What do you expect your answer to be?! -in

Answer 1

Area Tん (inB meas Let painp aes - an中 fam sin &-mens ees sin8-psinpess (-elue d = Amea Th aosee -) d 2 AL 2 p cot f-tanm-caf (o- L 2 2 C1tm of (eot m) + I 2 C1+m mrt) 2Hm 2 m /Note ca alauses P .yin itfre t

reoso fan Fh= 0,then tan o d tan h then hat Cnear yuales See that Hear ba e The max mum rana Arca Vo TlA Ree de -tan

31 mater too erafuabing dees the acrea eosine) 3inno cos no sn ne 2 n2ne Gin ano 1 2 こみ Area .. (: -ees 4ngde TT sin 4ne 474

in tart t Thn ne) sinta de Area Thn de 74 Finana do 4nDTde -coS 16 hn n 4n 1 4 in 27 Sin. 26 2n 1 2n 16 32n (1 cl