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Describe algorithms for drawing a graph on paper or on a display given the vertices and edges of the graph. What considerations arise in drawing a graph so that it has the best appearance for understanding its properties?
A tank initially contains 10 gallons of brine in which 3 pounds of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 2 gal/min. The mixture is well stirred and ows out of the tank at the rate of 1 gal/min.
Suppose a corporation wants a large picture to hang in its lobby in a space that is 90 ft.². What should be the dimensions of this picture if it is in the shape of a Golden Rectangle?
evaluate the multiple integral under given condition using spherical coordinate.let t be the three dimensional region
What is the expected value of the random variable X - 3? What is the expected value of (X - 3)2? What is the variance of X?
How do you determine whether an ordered pair is a solution to a linear equation? Can you demonstrate with the below examples?Determine whether the ordered pair is a solution to the given equation.
each letter in the diagram represents a unique digit and the letter O represents zero. What digit does each letter represent?
Find the rate of change of f at the point (1, π/6) in the direction (4, - 3). Find the vector u that maximises Duf (1, pi/6) and find the value of Duf (1, pi/6) for that u.
It takes you 50 seconds to walk from the first(ground) floor of a building to the fourth floor. How long will it take to walk from the first floor to the eight floor( at the same pace, assuming that all floors have the same height)
Suppose that in a particular circuit, L = 0.4 Henrys, R = 0 Ohms, C = 0.1 Farads and V = 110sin(ωt) Volts, where ω ∈ R. Initially the charge on the capacitor is 1 Coulomb and there is no current in the circuit. Write down the differential equation ..
a metal storage tank with volume 9 pi ft^3 is to be constructed in the shape of a right circular cylinder surmounted on the top by a hemisphere. what dimensions will require the least amount of material.
the area of a rectangle is 991cm squared if 991 is a prime number, what are the whole number dimensions of the rectangle?
Provide one business-related example each, with explanation, for mutually exclusive and independent events.
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