MAT102H5 Quiz: Quiz1A-sol
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MAT102H5 Full Course Notes
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Mat102f - introduction to mathematical proofs - fall 2015 - utm. Show your work, and clearly explain your arguments. If three boys eat three donuts in three minutes, then one boy eats one donut in three minutes. Similarly, one girl eats one donut in four minutes. In twelve minutes, one boy eats four donuts, and one girl eats three donuts. Therefore, twelve boys and twelve girls eat 12 4+12 3 = 48+36 = 84 donuts in twelve minutes. 2. (a) show that for any two real numbers x and y , we have (4 marks) For any real number a we have a2 0 , and so if x and y are real numbers, we observe that (2x 3y)2 0. 12xy 4x2 + 9y2 , and after dividing both sides by 6 , we get. From the agm inequality, we know that a b a+b. 2 for any nonnegative numbers a , b .
