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Consider the sphere (x - a)2 + (y - b)2 + (z - c)2 = d2 and a point P = (x0, y0, z0) not lying on the sphere. Use Lagrange multipliers to show that the shortest line segment connecting P to the sphere is that which extends through the center of the sphere.
If the width is doubled, fifty extra feet of fencing will be need to keep out the creatures. What are the dimensions of the original garden?
if a patient weighing 70kg requires 210mg of this medicine, then what is the amount of medicine requires for a patient weighing 80kg?
How many are interested in exactly one kind of show?
Estimate the relative error in the calculated surface area.
If {Phi_0, Phi_1, ..., Phi_n,...} are orthogonal polynomials in which are normalised to be monic (i.e. have leading coefficient equal to 1) show that ||Phi_k||
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with a diameter 50m. (Answer should be in cubic meters, rounded to two decimal places.)
Customers selecting one of these cars have a choice of three engine sizes, four body styles, and three color schemes. How many different selections can a customer make?
How can inequalties and equations help a business maximize cot and profit?
A child with an ear infection is given a 200-mg ampicillin tablet once every four hours. About 12% of the drug in the body at the start of a four-hour period is still there at the end of that period. Calculate the quantity of ampicillin in the body r..
a person collects coins nickels dimes and quarters in a jar. at the end of the year they emptied the jar and found that
What are all the possible dimensions for boxes that will hold exactly 2oo one-inch cubes?
what is the probability of getting someone who has been in a car accident?
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