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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.
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
Maclaurin Series Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specifi
subtract 20and 10,and then mutiply by 5
A long distance calls costs x cents for the first minute and y cents for every additional minute. How much would a 5-minute call cost? The cost of the call is x cents plus y ti
F(x)=2x+3
Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent
what are cos and sin ?
A plane is flying at 200 mph with a heading of 45degrees and encounters a wind mph from the west. What is the velocity and heading?
Can you explain slope and Slope is measured as rise/run?
Determine the mean of the subsequent numbers: Example: Determine the mean of the subsequent numbers: 5, 7, 1, 3, 4 Solution: where x' =
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