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An open box having a volume of 162 in.3 is to be constructed. If the box is to include a partition that is parallel to a side of the box, as shown in the figure, and the amount of material used is to be minimal, what should be the dimensions of the box?
if the radius of a circle is 14 inches and the arc of the circle is 30 degrees. what is the area of the shaded sector in between?
A man rows a boat 420 feet upstream against a constant current in 14 minutes. He then rows 350 feet downstream (with the same current) in 7 minutes. Find the speed of the current and the equivalent rate at which he can row in still water. Find spe..
Find the nodes x_i and the weights w_i so that the Gaussian quadrature of the sum from i=1 to 2 of (w_i) f(x_i) approximating the integral from -1 to 1 of f(x)dx is exact when f(x) is a polynomial of as high degree as possible.
Statistical procedure for developing a mathematical equation.
a company's total cost in millions of dollars,is given by c(t)=280-30e^-t where t= time in years, find the marginal cost when t=3
Probability of Coins Drawn, Suppose you have 6 nickels, 4 dimes, and 2 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that
Suppose that 740 ft of fencing is used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle. (In the blue outline represents the fencing.) Find the dimensions of the corral with maximum area.
Points A and B move along the x- and y-axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing, and is it increasing or decreasing, when OB=2r and B is moving toward O at ..
Why does the graph of the basic exponential function lie entirely above the x-axis?
Write computer code to determine the steady state temperature at the five co-ordinates in the rectangular region: (a/4,b/4), (3a/4,b/4), (a/4,3b/4), (3a/4,3b/4), (a/2,b/2) using the first 100 terms of the series solution (n = 1 to 100).
In the class, there are 12 freshmen, of whom 8 are males and 15 sophomores, of whom 5 are females. If one student is selected at random, what is the probability of selecting a freshman or a female?
A ball thrown vertically upward at time t=0(s) with initial velocity 80 ft/s and initial height 96ft and height function of y(t) = -16t^2 + 80t + 96. What is the max height attained by the ball?
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