Provide an appropriate response.It can be shown that a hyperbola with center at the origin, foci at F'(-c, 0) and F(c, 0), and equation 
has equation 
. Use this result to find an equation of a hyperbola with center at the origin, foci at (-4, 0) and (4, 0), and absolute value of the distances from any point of the hyperbola to the two foci equal to 4.
A. 
- 
= 1
B. x2 - y2 = 4
C. 
- 
= 1
D. 
- 
= 1
Answer: C
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Solve the problem.A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A platter takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 129 hours for prep time, 77 hours for painting, and 108 hours for firing, how many of each can be made?
A. 6 serving bowls, 3 platters, 7 bread baskets B. 8 serving bowls, 7 platters, 4 bread baskets C. 7 serving bowls, 6 platters, 3 bread baskets D. 3 serving bowls, 7 platters, 6 bread baskets
Answer the question.The graph below shows the level curves of a differentiable function f(x, y) (thin curves) as well as the constraint g(x, y) = 
- 
= 0 (thick circle). Using the concepts of the orthogonal gradient theorem and the method of Lagrange multipliers, estimate the coordinates corresponding to the constrained extrema of f(x,y).
A. (1.5, 0.2), (0.7, 1.3), (-1.5, 0.2), (-0.7, 1.3), (-1.5, -0.2), (-0.7, -1.3), (1.5, -0.2), (0.7, -1.3) B. (1.1, 1.1), (-1.1, 1.1), (-1.1,-1.1), (1.1,-1.1) C. (1.5, 0), (0, 1.5), (-1.5, 0), (0, -1.5) D. (1.3, 0.7), (-1.3, 0.7), (-1.3,-0.7), (1.3,-0.7)
Solve.If an earthquake measured 
on the Richter scale, what was the approximate intensity of the earthquake? The magnitude of an earthquake of intensity I is defined as 
, where Io is a minimum level for comparison.
A. 50,000,000 B. 2400 C. 63,000,000 D. 6,300,000
Fill in the blank with one of the words or phrases listed below.
The LCM of the denominators in a list of fractions is called the 
.
A. prime number B. composite number C. least common denominator D. numerator