Question

DEO Finding Numbers In Exercises 5-10, find E u two positive numbers that satisfy the given DEP requirements 5. The sum is S and the product is a maximum. 6. The product is 185 and the sum is a minimum. 7. The product is 147 and the sum of the first number plus three times the second number is a minimum. 8. The sum of the first number squared and the second number is 54 and the product is a maximum. 9. The sum of the first number and twice the second number is 108 and the product is a maximum. 10. The sum of the first number cubed and the second number is 500 and the product is a maximum. OSO TER Sa Maximum Area In Exercises 11 and 12, find the length and width of a rectangle that has the given perimeter and a maximum area. tanny 20 11. Perimeter: 80 meters 12. Perimeter: P units O TO Minimum Perimeter In Exercises 13 and 14, a find the length and width of a rectangle that has Od the given area and a minimum perimeter. 13. Area: 49 square feet 14. Area: A square centimeters 99 DEMO Minimum Distance In Exercises 15 and 16, SESVE find the points on the graph of the function that are 2. closest to the given point. 15. y - x. (0.3) 16. y = x2 - 2.(0.-1) 17. Minimum Area A rectangular poster is to contain 648 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be I inch. What should the dimensions of the poster be so that the least amount of poster is used? 18. Minimum Area A rectangular page is to contain 36 square inches of print. The margins on each side are to be 1 inches. Find the dimensions of the page such that the least amount of paper is used. 19. Minimum Length A farmer plans to fence a rectangular pasture adjacent to a river (see figure). The pasture must contain 405,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What dimensions will require the least amount of fencing? in

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Answer 1

5. sum=s Product is maaimum aty=s y=s-a P=ay=als-a)=sa-ae² plla) = 5611 - 2a = 5-2a Pl(a)=0 S-2a=0 a-ş plla)=0-2=-2 Product maalmum at a y = S- colo colo The two numbers al 6. Product = 185 sum is a minimum ay= 185 = 185 a sla) = aty - at 185 sta) = 1+(854= 1-185 s'(a) = 0 1-188 -0 a?= 185 a: 1185 gilla) = 0–185 (-) - 3.78 $111@) at a: 1195 = 370 (11853 do Sum is minimum at a=5185

(L-Re Səя»ть оң ә4. 8- 47 = 7 minitum a= 9 Sun e ч%) at a = 91 - 88 50 ва - ( hh -о- (Ф) 8 1ът 1һу те оби - о- (20,8 hh - = (a hh +1 = (,8 h, + = (th) e+e = Re += 8 hws, o 6 995mm Pooəs au- Sawit 22047 shid eaguna 750 so ung Thiag LhI=he LhI= onpoed oL numbeos=1185, (185) two The я - 195 - 18% 3. — 185