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A trapezoid with bases 4 m and 8 m is partially submerged vertically in water so that the top is 1 m above the surface and the bottom is 1 m below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it.
Would someone be able to explain to me how we would find antichains and chains of a powerset? For example, if we had the power set of 4 - P([4]) then how would we derive the antichains, and symmetric chains?
Find the hydrostatic force (in lb) on one end of the tank if it is filled to a depth of 8 ft with gasoline. Assume the gasoline's weight density is 420lbft3 (In British units, "weight density" is the equivalent of g in SI units.)
Suppose T is a Mobius transformation such that the image of the real axis under T is the real axis. Prove that T may be written in the form T(z) = (az+b)/(cz+d) with a, b, c, and d real.
Explain the main differences among integers, rational numbers, real numbers, and irrational numbers. How are these used in everyday life? How would you explain the use of each to someone who did not know about the differences?
Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the 14.6-hour-per-week benchmark reported by BusinessWeek.
A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis.
What score does a patient at the 75th percentile receive? d. What percentage of patients score between 185 and 199?
In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants.
Is the surface integral of a closed surface (for example the surface is the cylinder x^2+y^2=9 between the planes z=0 and z=2, together with the top and the bottom) supposed to be 0?
He plans to pay the loan back in full in 5 months using his income tax refund. He can go to a finance company that will charge him 18% or to his uncle, who has greed to charge him 9%. Find the difference in the interest charges.
Find the minimum and maximum values of Z=6x+5y, if possible, for the following sets of constraints.
Use the distributive property to multiply. Then, if possible, simplify the resulting espression.
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