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Let S be the circle in the plane {(x,y) in R^2: x^2 + y^2 = 1} and f: S --> R be a continuous map. Show that there exists (x,y) on S such that f(x,y) = f(-x,-y).
Explaining how to derive the formula for the distance between two points -Prepare an essay of 1,000 words explaining how to derive the formula for the distance between two points in analytic geometry 3-space.
From a raft 50m offshore, a lifeguard wants to swim to shore and run to a snack bar 100m down the beach. If the lifeguard swims at 1m/s and runs at 3m/s, express the total swimming and running time t as a function of the distance
Determine the number of groups under a given condition and How many license plates can a state have if each license plate has 2 letters followed by 4 digits, if the first digit cannot be zero?
Determine if the given function can be extended to a continuous function at x=0. If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary).
How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards? A bagel show has onion, poppy seed, egg, salty, pumpernickel, sesame seed, raisin, and plain bagels. How many ways are there to choose:
Solve the equation on the interval.
Find the derivative of the given function by using chain rule of differentiation.
Vectors : Identities and Dot Products, How could you use the properties of the dot product to prove the following identities
Find the distance between the silo and tree from the given data - What is the distance between the silo and the tree, correct to the nearest meter?
Nilpotent transformation, Consider the transformation N: V->V. Let g be a vector such that N^k-1 does not equal 0, but N^k = 0. First show that the vectors g,N(g),N^2(g),..,N^k-1(g) are linearly independent
Discrete probability distribution
Probability - offspring, For a certain animal species, the probability that a female will have a certain number of offspring in a given year is given
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