Topic: Related rates

Hi, I have been sending these questions to the tutors again and again as they are not giving step by step explanations for each method. it is hard to follow up with their answer.\

if you could, please solve these questions in an easy manner and use a cam scanner to capture your work. Please keep tidy handwriting.

Q3. A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t=k, the height of the dough is = inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute. a) At time t=k, at what rate is the area of the circular surface of the dough increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (4 marks) b) At time t = k, at what rate is the height of the dough decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V=ar h) c) Write an expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of height h and radius r.1. A particle moves on the hyperbola xy=18 for time t20 seconds. At a certain instant, y=6 and -=8. Which of the following is true about x at this instant? a) x is increasing by 4 units per second. b) x is decreasing by 4 units per second. c) x is decreasing by 1 unit per second. d) x is increasing by 1 unit per second. 2. Suppose that x and y are differentiable functions of t and are related by the equation 3x2 =2y? + 4. Given that= tax = -1, find " when (x, y) = (-2, 3), so dx at a) -2 b) -1 W H 3. A local automobile dealer has found that advertising produces sales, but that too much advertising tends to "turn consumers off," resulting in reduced sales. On the basis of past experience, the dealer expects that the number V ( x ) of vehicles sold during a month is related to the amount spent on advertising by the function below. V(x) = - 0.1x3 + 2.2x2 + 1.2x + 15 (0 S x S 20), Where x is the amount spent on advertising (in tens of thousands of dollars). What is the point of diminishing returns? Hint: The point of diminishing returns is the inflection point a) (7.33, 102.58) in tens of thousands dollars b) (7.33, 452.22) in tens of thousands dollars c) (7.33, 712.14) in tens of thousands dollars d) (7.33, 911.56) in tens of thousands dollars