Hello,

I'm doing my math homework for cal 3 and I need some help with the following three problems. Please show me the steps so I can find my errors.

1.

. Suppose that the depth, h, of a lake below the point (m,y) on the surface is given by h(a:,y) = 10mg 333 20. The point (a), y) is the location of the duck on the surface of the lake where it: and y are measured in feet on the surface of the lake and h is the depth, measured in feet below the point (33,y). Suppose a duck is at the point (3, 2). (a) What will the instantaneous rate of change in the depth of the lake if the duck heads in the direction towards the point (6, 7)? Will the depth be increasing or decresing? No decimals in your answer please (in other words, provide an EXACT answer). (b) In what direction should the duck swim from the point (3, 2) in order for the depth to decrease most rapidly? Your answer should be in vector format. (c) How fast will the depth increase in the direction given in Part b? No decimals in your answer please (in other words, provide an EXACT answer). ((1) In what direction should the duck swim so that the depth remains the same? The depth, in feet, of a lake at a point 2: miles east and 3; miles north of a buoy is given by h(93, y) = 175 30x2 203,2. (a) A rowboat is 1 mile east and 2 miles south of the buOy. At what rate is the depth changing with respect to distance in the direction of the buOy? (b) The boat starts moving toward the buoy at a rate of 4 mph. At what rate is the depth of the lake beneath the boat changing with respect to time