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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just im
integrate sin(x) dx
Carmen bought 3 pounds of bananas for $1.08. June paid for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy?
Find the equation of the plane through (2, 1, 0) and parallel to x + 4y 3z = 1.
(1)Derive, algebraically, the 2nd order (Simpson's Rule) integration formula using 3 equally spaced sample points, f 0 ,f 1 ,f 2 with an increment of h. (2) Using software such
E1) Why do we shift the place by one, of the result in the second row of the calculation, when we multiply, say, 35 by 237 E2) Write down the algorithm for the multiplication of
a mixture of 40 liters of milk and water contains 10% water.how much water should be added to this so that water my be 20% in the new mixture
Can Slope is calculated as run-rise?
Differentiate following functions. g ( x ) = 3sec ( x ) -10 cot ( x ) Solution : There actually isn't a whole lot to this problem. We'll just differentia
2.When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the tw
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