Business Calculus

Q1

A box with an open top has a square base and four sides of equal height. The volume of the box is 441 ft . The height is 2 ft greater than both the length and the width. If the surface area is 301 ft-, what are the dimensions of the box? X The width (and length) of the box is ft.dy dx Assume x and y are functions of t. Evaluate dt for 2xy - 7x + 6y = - 240, with the conditions = - 12, x=6, y= - 3. dt dy dt (Type an exact answer in simplified form.)A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being pulled in at the rate of 3 feet Rope per second, how fast is the distance between the dock and the boat decreasing when it is 2 feet from the dock? 2 ft Boat Dock The distance between the dock and the boat is decreasing by feet per second when the boat is 2 feet from the dock. (Round to the nearest thousandth as needed.)Boyle's lair.r for enclosed gases states that if the volume is kept constant, the pressure P and temperature T are related by the equation T=k where k is a constant. If the temperature is increasing at4 kelvins per hour, what is the rate of change of pressure when the temperature is 150 kelvins and the pressure is 300 pounds per square inch? The rate of change of pressure is D pounds per square inch per hour. (Simplify your answer.) A 1}foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down the wall when the bottom is 12 feet from the wall? The ladder is sliding down the wall at a rate of D fsee. (Type an integer or a simplied fraction.) A6.50-.ta|l man walks at 8.01] this toward a street light that is 17.0 it above the ground. Atwhat rate is the end of the man's shadow moving when he is 13.0 It from the base of the light? Use the direction in which the distance from the street light increases as the positive direction. The end at the man's shadow is moving at a rate of D We. (Round to two decimal places as needed.) A retail store estimates that weekly sales 5 and weekly advertising costs 3: (both in dollars] are related by s = 40.001] 20,000 at _ 0.0:]qu advertising costs are $4,000, and these costs are increasing at a rate of $601] per week. Find the current rate of change of sales. . The current weekly u.) The current rate of change of sales is $D per week. (Round to the nearest dollar as needed.) A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C = 0.4x~ + 9,000. How fast is the cost per month changing when production is changing at the rate of 18 units per month and the production level is 70 units? Costs are at the rate of $ per month at this production level. (Round to the nearest dollar as needed.)The price p (in dollars} and demand x lor wireless headphones are related by K: 1001] 071p? The current price of $100 is decreasing at a rate 957 per week. Find the associated revenue function Rm] and the rate of change [in dollars per week) of revenue. Rip} = dV An oil tanker aground on a reef is fanning a circular nil slick about 0.1 toot thick. To estimate the rate a [in cubic feet per m'nute] at which the oil is leaking from the tanker, it was found that the radius of the sick was increasing at 0.33 foot per m'nute dR {N {a = 0.33} when the radius R was 506 feet. Find E using I: m 3.1-L [Type an integer or a decimal. Round to the nearest whole number as needed.)