Question

a. Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian abc-coordinate system is - (3) a + b + c that is, the geometric mean of three nonnegative numbers is less than or equal to their arithmatic mean. b. Using part a show that, for nonnegative numbers a, b, and c, (abc) O A. a? + b2 + c s OB +25[*3) 3 ~ sakb²c² OC. 13 sa? + b2 + c 00. dve [6*** 4) ] 3 What operation should be done to both sides of the inequality to eliminate the cube operation being done to the fraction? O A. Divide both sides by 3. OB. Take the cube root of both sides. C. Cube both sides OD. Multiply both sides by 3 Which of the following substitutions, when performed on the inequality determined two steps ago, will result in an inequality equivalent to the inequality to be proved in part (b)? O A. Substitute x, y2 and 22 for a, b and c respectively. OB. Substitute x, y and z for a, b and c respectively C. Substitute x, y2 and 22 for a?, b2 and ca respectively, OD. Substitute x, y and z for a?, b2 and respectively. Click to select your answer. ?

Answer 1

com a) we have Maximize f(a, b, c) = a 2 b²c² subject to gla,b,c) - a² + b² +c²= 2. Thello pf = 2 + 3 + pf = 206?czi + 2a2bc2j+ 2025?c k + and og 2 it do gok Tg = 2ait 2bj + 20k we get la lihat If - dig 2 a 6² ² azad 2a²bc²= 2 bd 2 a²6² c ² = 20 2a2b??. 2031 2b²x = 2 c²x

we hare يعت 1 = م م و د 0 :A الدعمها then ه= 22 م 1 = ه کم عمخمخمخلوطيقاع ایع څه+ هغه نلرطبقلمه همه 2ر = 2و3 = ه و فرما دلمطبقلم وهمي maximum value of a²b²c² Thi i on sphere of radiis a cented at ouges

. 2و b) since the point Ja, o, 5.) in sphure it atbtc = Move over by part al we hare رچر) - (الحوطحيفلحاسطه چربه قارعهما عهده حطم طمعا

Nguy w what operation should be done to both sides of une inequality to eliminate cube operation being done to une fraction? Take une cube root of both sides in which of the following substitution when performed on une inequality atturmined two seths ago, mull result an an inequality equivalent to be frored in pod b)3 D) substitule xy and for a2, 6² and respectively.