Evaluate dz using the given information. z= 5x2 + 8xy + 7y; x=3, y= -7, dx=0.08, dy = - 0.03 Set up the total differential of z. dz = ( . dx + ( - dyEvaluate dw using the given information. 5x2 + 4y2 W= z+ 2 ; X= - 6, y = 5, z= 1, dx = 0.01, dy = - 0.06, dz = 0.02 dw ~ (Do not round until the final answer. Then round to four decimal places as needed..)Approximate the volume of aluminum needed for a beverage can of radius 3 cm and height 13 cm. Assume the walls ofthe can are 0.07 cm thick. The volume of aluminum needed is cm3. (Round to the nearest hundredth as needed.) A piece of bone in the shape of a right circular cylinder is 9 cm long and has a radius of 1.8 cm. It is coated with a layer of preservative 0.08 cm thick. Estimate the volume of preservative used. . . . The volume of the coating is approximately cm3 (Do not round until the final answer. Then round to three decimal places as needed.)b The number of liters of blood pumped through the lungs in one minute is given by C = E' where b is quantity of oxygen used bythe body in one minute, a is the quantity of oxygen per liter of blood that has just gone through the lungs, and V is the quantity of oxygen per liter of blood that is about to enter the lungs. Suppose a =145, b = 195, and v =110. Estimate the change in C if a becomes 150, b becomes 190, and v changes to 125. Find the equation for the total differential of C to estimate the change in C. dC= da+ db+ dv The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x,y) is the location of the starter (in meters), (0,p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4, - 4). Answer parts a and b below. p Swimmer 1 x 2 + ( y - P ) 2 t(x,y,p,C) = - X 331.45 + 0.6C -41 Starter (4,-4) . . . a. Calculate t(4, - 4,25,25) and t(4, - 4,15,25). Could the difference in time change the outcome of a race? t(4, - 4,25,25) = (Round to five decimal places as needed.)