Question

The orthogonal trajectories of the family of curves 22 = 2y - 1+ Ce-24, where is an arbitrary constant, is given by the family of curves xy² +k where k is an arbitrary constant 4 None of them za y - where k is an arbitrary constant +k 4 o 22 + y + k, where K is an arbitrary constant 4 0 3+ y2 where K is an arbitrary constant Question 4 3 pts Newton's Law of Cooling states that the rate of change of the temperature of a cooling body is proportional to the difference between the temperature of the body and the constant temperature of the medium surrounding the body, Apply this law to the following problem: At 10:00 am, a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant the temperature of the coffee was 180°F, and 10 minutes later it was 160°F. If we assume that the constant temperature of the kitchen was 70°F, what was the temperature of the coffee at 10:15 am 101 11 - None of them 0 F 10(7+ **) ° +(10+70) (10 + 27/11 F O 7 10+

Answer 1

2 3 2 =27_17 Ce-ay > za 7 28 में Zs aa = 2. de -20.energie en [differentiating both sides w.rt. a] - Cierry) a ne Czy-x2. se 1-cê 299 2y-ae Now, replacing (1) by G day we get; (27-x²). (de) 2²-24 → dva + y ( ) Salade the integrating factor is; M(x) So, 2 x? de la So; 2. y = faldet k ► kg - + * So, the orthogonal to ajectory is; 2y = 2 + k, skee, K is an arbitrary dy 2 3a Elna e Feln (22) 2 e ge 3 + 2a.g a constant.