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Quiz 6 - Math 53, section 213
1. Use a double integral to find the area of the region of points that lie inside the circle (x - 1)2 + y2 = 1 and outside the circle x2 + y2 = 1.
2. Find the surface area of the part of the plane 3x + 2y + z = 6 that lies in the first octant.
Ahmed has first half of a treasure map, which indicates that the treasure is buried in the desert (2x + 6) paces from Castle Rock. Vanessa has the other half of the map.
Will this use compound interest? If not, how can I word the problem where the interest will compound?
Q: Consider the triangle with vertices at (0,0=x1, (2,0)=x2, and (1,1)=x3. Show that u={(2/3),(1/2)} can be written in the form u=a1x1+a2x2+a3x3, where a_i >= 0, i=1,2,3 and a1+a2+a3=1.
What speed is the lamp's spot moving as it passes the point where it is perpendicular to shore? How fast is the spot moving along the shore when the spot is 1 km from the point at which it is perpendicular?
Let A be a nonempty, bounded set of real numbers. Show, that sup A >inf A if and only if A contains at least two different points.
The standard deviation is 5 minutes. If a randomly selected freshman takes the exam,?nd the probability that he or she takes more than 32 minutes to complete the test.
The graph represents the results of a survey in which 400 people were asked to identify the TV channel on which they preferred to watch the evening news. How many more people preferred WWCN than WANR?
petros wishes to retire in 10 years from now. he has 250000 in his rrsp currently and will contribute 5000 at the
Write a plane equation for plane passing through P (1,2,3) and perpendicular to n = . Write a plane equation for plane passing through P(1, 2, 3), Q(-1,0,1) and R(0,0,1).
Assume that the average annual salary for a worker in the United States is $27,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following:
1. Let σ be the ruled surface generated by the binormals b of a unit-speed curve γ: σ(u, v) = γ(u) + vb(u). Show that the first fundamental form of σ is
Math 104: Homework 10. Construct a Taylor series expansion for the function f(x) = log(1 + x) at x = 0. By considering the remainder Rn(x), prove that the Taylor series agrees with f in the range -1/2
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