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Modeling With functions

1.7. Modeling With functions. Who was the roundest knight at King Arthur's Round Table?. Sir Cumference. From Words to Expressions. A number increased by 2 then cut in half 5 decreased by a number then tripled A number decreased by 7 then doubled. (n+2)/2. 3(5-n). 2(n-7).

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Modeling With functions

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  1. 1.7 Modeling With functions

  2. Who was the roundest knight at King Arthur's Round Table? Sir Cumference

  3. From Words to Expressions • A number increased by 2 then cut in half • 5 decreased by a number then tripled • A number decreased by 7 then doubled (n+2)/2 3(5-n) 2(n-7)

  4. Area of a Circle • We know…. Area=πr² • But…. What happens when we have the circumference and we have to find area??? • Well….

  5. Area of Circle Cont. • C= Circumference • Since C= 2πr we can solve for r to get r= C/(2π). Then we can substitute to get area: A= πr²= π(C/2 π))²= πC²/(4π²)= C²/(4π) • So … Area= C²/(4π) • Example: C= 8 so 8²/(4π)= 5.093

  6. Box Problem • A square of side X is cut out of each corner of an 8 in. by 15 in. piece of cardboard and the sides are folded up to form an open-topped box. How big should the cut-out squares be in order to produce the box of maximum volume? 8 x x 15

  7. Solution • Volume = Length x Width x Height • V = (15-2x) (8-2x) (x) • X = 1.667 inches

  8. Box Problem 2 • A square side is cut out of each corner from a 20cm by 8cm piece of cardboard to form an open-top box. Find the value of x for the box to have the maximum amount of volume.

  9. Solution • Volume = Length x Width x Height • V = (8-2x) (20-2x) (x) • X = 1.761 centimeters

  10. Box Problem 3 • Find the maximum volume. 10 X X 47

  11. Solution • Volume = Length x Width x Height • V = (10-2x) (47-2x) (x) • V = 526.847 units

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