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- 5. At a sunglass manufacturing company, the estimated average cost function for producing a new line of glasses is C(x)=x2-4x+20, where x is the number of units produced, in thousands. C(x) is measured in dollars. Estimate the rate at which the average cost is changing at a production level of 3000 units. 39.44. The dimensions of a rectangular plate are changing so that the plate maintain its rectangular shape at all times. If the length of the plate is increasing at the rate of 4 cm / s while its area remains constant at 100 square centimetres , determine at what rate is its width changing at the instant its width is 5 cm.
- 3. Suppose that Katanga Motors' share of the new cars sold in Ghana is charging at the rate of f (t) = -0.01875t2 + 0.15t – 12, (036. Net Savings A new smog-control device will reduce the out- put of sulfur oxides from automobile exhausts. It is estimated that the rate of savings (in millions of dollars per year) to the community from the use of this device will be approximated by S'(1) = -r² + 4t + 8, after i years of use of the device. The new device cuts down on the production of sulfur oxides, but it causes an increase in the production of nitrous oxides. The rate of additional costs (in millions of dollars per year) to the community after t years is approximated by C" (1) = a. For how many years will it pay to use the new device? b. What will be the net savings over this period of time?11. An cone-shaped icicle is melting at the constant rate of 5 cubic centimeters per minute. (a) Define appropriate variables and derive the related rates equation for the above situation. Do not simplify. (b) The icicle is shaped like a cone, with the height always 4 times longer than the diameter of the base. Determine how fast the height of the icicle is changing at the moment it is 4 cm long. Round only final answers to 2 decimal places.4. In the city of Calcary, temperatures tend to range from a low of –15" Celsius to a high of 30" Celsius. The number of days, in one year, that the city experiences temperatures below T degrees Celsius, is given by D(T) = 14e - 15 s Ts 30 dx -15 (a) As part of a project on reducing energy consumption due to heating you are asked to estimate the following quantity: The number of days, in one year, that the temperature in Calcary is below 0° Celsius. If you had to make sure to underestimate this quantity, which numerical integration method would you use? Justify.1) Suppose that the dollar cost of producing q extra-large pepperoni pizzas is C(q) = 2200 + 15q – 0.125q?. Find the marginal cost when 30 pizzas are produced.2. Newton's Law of Cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the temperature 7 of the surrounding medium: dT dt = -k(T-T). where k is a positive constant. (a) Solve this equation for T given that T(0) = To. (b) Take To > 7. What is the limiting temperature to which the object cools as t increases? What happens if ToRecommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning