Analyse convexe et optimisation by Michel Willem

By Michel Willem

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Below, we show the graph of the equation y = 2x + 3. 10 y x y −3 −3 −2 −1 −1 1 0 3 1 5 2 7 3 9 x -10 10 -10 The graph of the equation y = 2x + 3 Here is some useful terminology. The horizontal line in our picture is called the x-axis; the vertical line is the y-axis. The graph in this example is a line with slope 2 and y-intercept 3. The slope measures the steepness of the line. With a slope of 2, this says that as x increases by 1, then y increases by 2 (which you can see from the table). The y-intercept is simply the value of y when x = 0.

You can reconstruct the answer by stripping off the last two digits from the rest of the answer and calculating their average. Here, the larger number is (59 + 25)/2 = 84/2 = 42. To get the smaller number, subtract the last two digits of their answer from the larger number. Here, 42 − 25 = 17, as desired. The reason this works is almost the same explanation as before, except after step 5, the answer is 100( X + Y ) − ( X − Y ), where X − Y is the last two digits of the answer. Here’s one more example: if the answer is 15,222 (so X + Y = 152 and X − Y = 22), then the larger number is (152 + 22)/2 = 174/2 = 87 and the smaller number is 87 − 22 = 65.

Step 2. Add those numbers together. Step 3. Multiply that number by 10. Step 4. Now add the larger original number. Step 5. Now subtract the smaller original number. Step 6. Tell me the number you’re thinking of and I’ll tell you both of the original numbers! Believe it or not, with that one piece of information, you can determine both of the original numbers. For example, if the final answer is 126, then you must have started with 9 and 3. Even if this trick is repeated a few times, it’s hard for your audience to figure out how you are doing it.

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