MATH-1325-PHW_10, 2022-11-05 12:29 3 1. (10 points) Consider the following equation: xy' + 5 = 92 - 3y2 dx (a) Find in terms of a and y: (b) Evaluate - at (x, y) = (1, 1):MATH-1325-PHW_10, 2022-11-05 12:29 2. (10 points) Consider the following equation: In(x2 +y' - 6x) = 5x - 10 (a) Find in terms of a and y: (b) Evaluate - at (x, y) = (2, 3):5 MATH-1325-PHW_10, 2022-11-05 12:29 3. (10 points) Consider the following equation: yex-+3 = 5x In(2y - 7) Find - dy in terms of x and y: dx\fMATH-1325-PHW_10, 2022-11-05 12:29 5. (10 points) Consider the following equation: y lnx + xey = 1 (a) Find the relationship between- da at and at . (Do not solve.) dt (b) Find - at the moment when x = 1, y = 0 and aid = 4: dtMATH-1325-PHW_10, 2022-11-05 12:29 8 6. (10 points) A 17 feet ladder is placed against a building. The bottom of the ladder is sliding away from the building at a rate of 5 feet per second. Find the rate at which the top of the ladder is slipping down at the instant When the bottom of the ladder is 15 feet from the base of the building. MATH-1325-PHW_10, 2022-11-05 12:29 7. (10 points) A plane is flying away from you at 800 mph at a constant altitude of 4 miles. How fast is the plane's distance from you increasing at the moment when the plane is flying over a point on the ground 3 miles from you? 4 miles