Question

hi, im trying to do my calculus study guide, and im kind of confused about both.

3. 110 pts Find two positive numbers whose sum is 8 such that the sum of the cube of the first and the square of the second is a minimum. CITY 7 4. 115 pts) A student is drinking a milkshake with a straw from a cylindrical cup with a radius of 4 cm. If the student is drinking at a rate of 3.5 cm per second, how fast is the level of the milkshake dropping? (Note Volume of a cylinder is found by V = #r?h] 5. [10 pts) Find the following

Answer 1

6 let the two Numbers are & and y x+y=8 y = 8-x S + ye 5x + (8-4) 2 Differentiating both side wort a se 32² + 2(8-2) × (-1) Ret s'zo to Find critical o= 3x² + 2x-16 x= 2 and -8 us using chain Rule paints S" : 64 +2 when x=2 ss0 Hence minimum accurs at x2 x = 2 a toly = 8 Numbers are (2 and 6 l

4) (liven ilven volume is V decreasing at ca . -3.5 V = 77th 2.5 = 7*x (4) 2 db de dh. - 0.07 cm/s Hence level of milkshake is dropping at 0.07 con/s. a) ein In (2) .. & x²1 In(a) using L'Hospital Rule Leat at alem - 20 +) 2 (1+ 5) x x215x x
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