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Question 1 - A cube has sides of length 4. Let one corner be at the origin and the adjacent corners be on the positive x, y, and z axes.
If the cube's density is proportional to the distance from the xy-plane, find it's mass.
Question 2 - Evaluate the integral
0∫1 0∫x 0∫1+x+y f(x, y, z) dz dy dx
where f(x, y, z) = 1.
starting at 8 A.M. determine the number of times in the next 24 hours for which the hour and minute hands on a clock coincide?
Find the value of a so that the function f(x) = xeax has a critical point at x = 3.
Write, as a set of ordered pairs, a function f that is a bijection from V1 to V2, satisfying the following condition: if x and y are elements in V1 such that {x,y} is in E1, then f(x) and f(y) are elements in V2 such that {f(x),f(y)} is in E2, and..
How many bunches of a half dozen can be formed if each bunch must contain at least one rose of each color?
Jen invested a total of 500 dollars, part of it at 9 percent interest and the rest at 10 percent. If 48 dollars was earned from the investment, how much money was invested?
X and Y are sets. ζu refers to the usual topology, ζH is the half-open interval topology. ζC is the open half-line topology, ζF is the finite complement topology and ζcc. is the countable complement topology. R is the set of real numbers, Z is the ..
On which interval is the average rate of change greater: 0 = x = 2 or 6 = x = 8?
A shipment of 120 computer cases that contains 5 defective cases was sent to an assembly plant. The quality control manager at the assembly plant randomly selects 5 cases and inspects them. What is the probability exactly one case is defective?
Founded in the early 1980s, the Vermont Teddy Bear Co. designs and manufactures American-made teddy bears and markets them primarily as gifts called Bear-Grams.
Vectors : Identities and Dot Products, How could you use the properties of the dot product to prove the following identities
A thermometer reading 8°C is brought into a room with a constant temperature of 20°C. If the thermometer reads 18°C after 5 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: U = T..
A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answ..
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