Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. Which is NOT part of an accurate description the region given by the polar bo

ID: 2832776 • Letter: 1

Question

1. Which is NOT part of an accurate description the region given by the polar bounds 2 r S 5,3m/4 5m/4. (A) It is a wedge shaped region in between circles of radius 2 and 5 (B) It starts at an angle of 7 above the negative x-axis and sweeps clockwise T/4 to an angle of 4 below the negative x-axis. (C) The edge of the inner circle is not included (D) The edge of the outer circle is included 2. When converted to rectangular coordinates, the points (a) (2,2T/3), (b) (4,3T), (c) (-2, -5T/6) have rectangular coordinates (a) (A, B), (b) (C, D), (c) (E, F) respectively. Four of the numbers A, B, C, D, E, F are integers (the other two are both V3). Enter the sum of those four integers. 3. When converted to Cartesian form, the curve r 2 sin 6 2 cos 0 has the form (z -A)2 (y B)2 2. Enter the sum A B 4. When converted to polar form, the curve 2 y 9 has the form r A. What is A?

Explanation / Answer

1) figure int his question area between circle of radius 2 and radius 5 but for angle given

so B) option is not correct

2) coordinates are

A = 2 cos 2pi/3 = -1

B = 2 sin 2pi/3 = sqrt3

C = 4 cos 3pi = -4

D= 4 sin 3pi = 0

E = -2 cos(-5pi/6) = sqrt 3

F = -2 sin (-5pi/6) = 1

sum of those fours integers = -1-4+0+1 = -4

c) r = 2sin z + 2 cos z

as we know r = x^2 + y^2

and r cosz  = x and r sinz = y

r^2 = 2rsinz + 2rcosz

x^2 + y^2 = 2 x + 2y

x^2 -2x + y^2 - 2y = 0

(x-1)^2 + (y-1)^2 = 2

So A= 1 and B=1

A + B =2

d) let x= r cosz

y = r sinz

so putting in equation

we get r^2 cos^2(z) + r^2sin^2(z) = 9

r^2 [cos^2(z) + sin^2(z)] = 9

r^2 = 9

r=3

so A= 3