Provide an appropriate response.(a) Graph the curves r = 
and r = 
.(b) Find polar coordinates of the points of intersection of the curves in part (a).(c) Show that at the points of intersection the tangent lines to the curves are perpendicular to each other.
What will be an ideal response?
(a)
(b) The curves intersect in two points. In polar coordinates, these points may be represented by 
and 
.
(c) For r = 
, 
= -cot 
. For r = 
, 
= tan 
. Thus the slopes of the tangent lines to the curves at both of the points of intersection are negative reciprocals of each other so the tangent lines are perpendicular.
You might also like to view...
Solve the problem.Find the mass of a thin infinite region in the first quadrant bounded by the coordinate axes and the curve 
if 
.
A. 
B. 
C. 
D. 
Solve the problem.Find the length of a rectangular lot with a perimeter of 108 m if the length is 8 m more than the width. 
A. 54 m B. 31 m C. 23 m D. 62 m
Test for symmetry with respect to q = p/2, the polar axis, and the pole.
A) symmetric with respect to the pole
B) symmetric with respect to the polar axis
C) symmetric with respect to q = p/2
D) symmetric with respect to the pole and the polar axis
E) symmetric with respect to the pole and q = p/2
At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are:Less than 17 seconds
A. 98% B. 97.5% C. 84% D. 2.5%