If the equation represents a hyperbola, find the center, foci, and asymptotes. If the equation represents an ellipse, find the center, vertices, and foci. If the equation represents a circle, find the center and radius. If the equation represents a parabola, find the focus and directrix. y2 - x2 - 4y + 10x - 57 = 0
A. C: (5, 2); F: (0, 2 + 6
), (0, 2 - 6
); A: y - 2 = x - 5, y - 2 = -(x - 5)
B. C: (5, -4); F: (6
, 0), (- 6
, 0); A: y =
x, y = - 
x
C. C: (5, 2); F: (5, 2 + 6
), (5, 2 - 6
); A: y - 2 = x - 5, y - 2 = -(x - 5)
D. C: (-1, 2); F: (6
, 0), (- 6
, 0); A: y = x, y = -x
Answer: C
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Find the general solution of the equation. Express the solution explicitly as a function of the independent variable.u'(x) = e3x-6u
A. u = 6 ln
+ C
B. u = 
ln
C. u = 
ln
+ C
D. u = 6 ln
Solve the problem.The surface area of a sphere is f(x) = 4?x2 square inches, where x is the radius of the sphere in inches. Find the inverse of this function.
A. f-1(x) = 2
B. f-1(x) = 
C. f-1(x) = 2
D. f-1(x) = 
For the year 1840, find the standard quotas for the city districts given in table that shows the population (in thousands) over the years. Assume there are eight council seats. Round the answers to three decimal places. Year Total District A District B District C District D District E 1790 50 32 2 6 6 4 1800 83 61 2 6 7 7 1840 747 516 10 197 5 19 1900 3,431 1,850 194 1,167 153 67 1940 10,155 1,890 1,395 2,701 1,297 174 1990 7,325 1,488 1,204 2,301 1,953 379 2000 8,007 1,537 1,333 2,465 2,229 443 ? District A District B District C District D District E __________ __________ __________ __________ __________
What will be an ideal response?
Find the nth term an of the geometric sequence.an = 
; 1, - 
, 
, . . . .
A. n = 11 B. n = 6 C. n = 8 D. n = 13