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Compactness.
Suppose K is compact set. Prove that K is of content zero if and only if is of measure zero. Give a counter example if the compactness assumption is dropped.
Area of region using definite integrals
Find the area under the curve y= x^2 and find the area under the curve y = x^3 over the interval [0,1]
A window frame that seems rectangular has height 408 cm, length 306 cm, and one diagonal with length 525 cm. Is the window frame really rectangular? Explain please.
A wheel of radius 2 feet begins moving down a ramp of height 6 and length 24 feet , turning at 23 revolutions per minute clockwise as it does. At time t = 0 the point P on the wheel is at [0, 6]
What is the total dollar amount to be repaid on the loan, including principle and interest, for the entire year?
If 80% of a radioactive element remains after 250 million years, then what percent remains radioactive after 600 million years? What is it's half life?
When you subtract one number from another, the answer is always less than both of the numbers in the subtraction problem. Support or disprove this statement with examples.
Car license plates in California take the form of 1RTY345. If zero cannot be used in the first position and repeats are allowed in the other 6 positions, how many license plates are possible?
If a ball is thrown directly upward with a velocity of 28 ft/s, its height (in feet) after t seconds is given by y = 28t - 16t2. What is the maximum height attained by the ball? (Round your answer to the nearest whole number.)
what length is the hypotenuse of a right angled triangle if the base is 123inches,the short side is 114inches and the angle opposite the right angle is 41degrees.
Define the function f: (0, 1) -> A as follows: For x in the open interval (0,1), let f(x) be the element of A with the property that for every positive integer k, the digit i_k in the kth decimal place of f(x) is the least i in I such that x has a..
find the length of the room if the cost of carpeting 24 m broad room with 150 cm wide carpet at Rs.16 per metre is Rs.3840.
Andy begins walking north from an intersection at (v+3) ft/s. After 10 seconds, he is 100 ft north of the intersection. What is the value of v?
The yearly production of a 6 foot is 22 pounds of oranges. A 16 foot tree produces 86 pounds.
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