Find a polar equation of the conic with the given characteristics and with one focus at the pole.
Conic
Ellipse
Vertices
a. 
b. 
c. 
d. 
e. 
c.
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Express the integrand as a sum of partial fractions and evaluate the integral.
dx
A. ln 
- 
+ C
B. ln 
- 
tan-1 
- 
+ C
C. - 
tan-1 
- 
+ C
D. ln 
- 
tan-1 
+ C
Simplify the expression.3y(xy + y) - 9y 2(x - 2 + 5y) + 2(y 3 + y 2)
A. - 6xy 2 + 21y 2 + 20y 3 B. - 6xy 2 + 23y 2 - 43y 3 C. 12xy 2 + 21y 2 - 43y 3 D. 6xy 2 + 21y 2 - 20y 3 E. none of these
Solve the problem.A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level ground, find its rate in the mountains.
A. 80 mph B. 20 mph C. 50 mph D. 40 mph
Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
A. 
- 
i
B. - 
- 
i
C. - 
i
D. 
- 
i