Math_270_Test_4_Hints

# Math_270_Test_4_Hints - What are those two points in this...

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Math 270 Test 4 – Hints Due Friday, July 25 Here are some hints for the test. 4. In general, the distance between two points 1 1 2 2 ( , ) and ( , ) x y x y is given by ( 29 ( 29 2 2 1 2 1 2 d x x y y = - + - . What is the distance from a point (x, y) on the curve y = x 2 and the point (6, 3)? What x-value minimizes this distance? 7. Look back at section 4.5 # 20. This problem is identical except for the area of the little rectangle. 8. First, write out a formula for the sum of the two areas. The circumference of the circle is x, so what is the radius? Use that radius to find the area of the circle. The perimeter of the square is L – x, so what is the length of one side? Square the side length to find the square’s area. Add those two areas to get the total. You need to find the x-values that minimize and maximize the total area, but the formula has only one critical point. Other than CP’s, where can a global max or min occur?
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Unformatted text preview: What are those two points in this particular case? Now, you have three possibilities for the two x-values you need. Plug them in and see which one gives you the largest and smallest area values. Keep in mind that with fractions, if the denominator gets bigger, the fraction gets smaller; more precisely, if A < B, then k k A B for any constant k such as 2 4 L k = . 10. As the water level drops, the radius decreases, so you cant just use 2 1 3 V r h = and treat r as a constant. However, you can write r as a very simple function of h using similar triangles. The two triangles in the picture are similar, so the ratio r/h is constant. When h = 10, you know r = 6, so what is that constant ratio? Use it to write r in terms of h, then substitute back into the volume formula....
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## This note was uploaded on 05/18/2011 for the course MATH 270 taught by Professor Vakarietis during the Summer '08 term at University of Louisiana at Lafayette.

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