Perform the indicated operations and simplify the result. Leave the answer in factored form.
- 
A. 
B. 
C. 
D. 1
Answer: C
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Answer the question.Describe the results of applying the method of Lagrange multipliers to a function f(x, y) if the points (x, y) are constrained to follow a curve g(x, y) = c that is everywhere perpendicular to the level curves of f. Assume that both f(x, y) and g(x, y) satisfy all the requirements and conditions for the method to be applicable.
A. The results cannot be generally predicted. Specific expressions for f(x, y) and g(x, y) = c are required. B. Generally, local extrema of f(x, y) occur at points on the curve g(x, y) = c where the curve becomes tangent to a level curve of f(x, y). Since the curve defined by g(x, y) = c is everywhere perpendicular to the level curves of f(x, y) for this particular case, it is never tangent to a level curve, and there are no local extrema along g(x,y) = c. The method of Lagrange multipliers will fail to find any local extrema since there are none. C. Since ?f is everywhere parallel to ?g, there will be a single local minimum and a single local maximum along g(x, y) = c. Applying the method of Lagrange multipliers should identify the locations of these two local extrema. D. Since ?f is everywhere parallel to ?g, every point on g(x, y) = c is a local extremum. Applying the method of Lagrange multipliers should yield the equation g(x, y) = c.
Solve.The air pollution, y, in appropriate units, in a large industrial city has been growing as shown by the graph below, where x is time in years from 1990. That is, x = 0 represents 1990. Approximate the air pollution in the year 2005 (x = 15) to the nearest thousand.
A. 20,000 B. 18,000 C. 15,000 D. 22,000
For the given bond, whose interest rate is provided, find the semiannual interest payment and the total interest earned over the life of the bond.$29,000 First Income Fund 11-year bond at 2.865%
A. $41,542.50; $913,935.00 B. $414.70; $9123.40 C. $830.85; $9139.35 D. $415.43; $9139.35
Solve the equation. Express radicals in simplest form.(x + 4)2 = 20
A. -4 + 2
, -4 - 2
B. 2
, -2
C. 2
- 4, 2
+ 4
D. -4 + 2
, -4 - 2