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Let E; f be 2 points in the plane such that EF has length 1, and let L be a continuous curve from E to F. A chord of L is a straight line joining two points on L. Prove that if 0 < E; F < 1,and L has no chords of length a or b parallel to EF, then L has no chord of length e + f parallel to EF. Prove that K has chords of length 1/Xparallel to EF for all positive integers X. Must L have chords of length r parallel to EF for any real r with 0 < r < 1?
The trough is full of water (density ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use as the acceleration due to gravity.)
a recreational club has 12 members.a. in how many ways can the club choose 6 members to form a volleyball team? show
Records indicate that t hours past midnight, the temperature at the local airport was f(t) = -0.3t^2+4t+10 degrees Celsius. what was the average temperature at the airport between 9:00am and noon?
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = -3.
what will happen to the volume of a cube with a side measurement of 6cm if its length is double? note the cube retain its shape.
A surveyor fins that a tree on the opposite bank of a river, flowing due east, has a bearing of N 22 degrees 30' E from a certain point and a bearing of N 15 degrees W from a point 400 feet downstream. Find the width of the river.
The trough in the figure is to be made to the dimensions shown. Only the angle theta can be varied. What value of theta will maximize the trough's volume?
The Sun is shining directly down a missile silo 1000 miles to your south, while at your location, the Sun is 36° from straight overhead. What is the circumference of Myrmidon? What is its radius?
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to describe the lighter coin using this number of weighings.
Describe the state space of this process. Explain why Xn forms a Markov chain and its transition probabilities.
A spherical balloon is inflating at a rate of 27 pi cubic inches per second. How fast is the radius of the balloon increasing when the volume is 112 cubic inches.
A cyclist travels 105 km in 7 hours going against the wind. He travels 133 km with the wind in the same amount of time. What is the rate of the cyclist in still air and what is the rate of the wind?
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