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a) Give an example of a quadratic polynomial, defined on the open interval (-5,3),which does not reach a maximum value?
b) Give an example of a quadratic polynomial, defined on the open interval (-5,3),which reaches neither a maximum nor a minimum value?
c) Give an example of a cubic polynomial, defined on the open interval (-5,3),which reaches both its maximum and minimum values?
A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?
A random variable defined on all real numbers has a probability density proportional to: c/ X2 + 1. What is c? What is the probability that the random variable lies between 0 and 1?
The family cat is also walking in the backyard. The line segment between the cat and the two trees are always perpindicular. Find the equation of the locus of the cat.
A one compartment vertical file is to be constructed by bending the long side of an 8 inch by 20 inch sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
Find the continuous-compounding nominal interest rate per annum (r) that is equivalent to a discrete-compounding interest (i) of:
Use the chi square test to find the listed occupations
Prove the given equations : sin6Θ+cos6Θ=1-3sin2Θcos2Θ
the difference of one less than a number and twice the number
The monthly charge for a waste collection service is 1280 dollars for 100 kg of waste and 2240 dollars for 180 kg of waste. Find a linear model for the cost, , of waste collection as a function of the number of kilograms, w.
A truck burns fuel at the rate (gallons per hr) of G(x) = 1/33(64/x+x/49) while traveling at x mph. If fuel costs $1.18 per gallon, find the speed that minimizes total cost for a 200-mile trip.
Sally wrote on her midterm exam that the definition of the limit is the following: The sequence {an} converges to the real number L if for every e>0 we have |an-L|
prove if two lines have a transversal which forms corresponding angles that are congruent then the two lines are
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