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a solid is generated by revolving the region bounded by y=.1x^2 and y=10 about the y-axis. a hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. find the diameter of the hole. round your answer to three decimal places.
Probability on normal distribution
Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R. Prove axioms (VS1)=For all x,y, x+y=y+x (commutativity of addition),
Find the minimum and maximum values of Z=6x+5y, if possible, for the following sets of constraints.
Define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx. is f integrable on [0,1]?
If the box is to have a volume of 72 cubic inches, find the length and width of the cardboard that must be used.
Find the maximum margin separating hyperplane by solving the dual lagrangian constrained optimization problem. What is the value of the margin?
Using the standard inner product in R^3, find two unit vectors that are orthogonal to u=(3,-2)
Find the probability of getting less than six correct answers.
A Midwestern company that produces a particular machine component has 3 factories, one each in Chicago, Cleveland, and St. Louis. 50% of the components produced come from the Chicago factory
Find a nonzero vector PQ with initial point P(-1,3,-5) such that u is opposite in direction to v = (6,7,-3). In other words, find the coordinates of Q.
The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.
Test using the traditional approach with α = 0.05
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