2. For a certain rectangle the length of one side is always three times the length of the other side. (a) If the shorter side is decreasing at a rate of 2 inches/minute at what rate is the longer side decreasing? (b) At what rate is the enclosed area decreasing when the shorter side is 6 inches long and is decreasing at a rate of 2 inches/minute?

Q: At high noon, boat A is exactly 30km due West of boat B. Boat A is heading South at a speed of 50…

A: From the given information, each boats travels 2.5 hours after noon and A is heading South at a…

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Find the…

A: To find the marginal revenue we find dr/dx

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: A cooperative society of farmers has 50 hectares of land for two crops, X and Y. Earnings for crops…

A: Given:  cooperative society of farmers has 50 hectares of land for two crops, X and Y. Earnings for…

Q: (5) Suppose 2 mg of a drug is injected into a person's bloodstream. As it metabolizes, the amount of…

A: Initially 2 mg of drug is injected and it decreases at the rate of 4% each hourWhen must the person…

Q: The length of the rectangle is decreasing at a rate of 5 centimeters per second, and its width is…

A:

Q: 4 If the cost of the machine is $14000, its salvage value is $1500 and its estimated useful life is…

A:

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: Formula of volume V=43πr3 Given: Radius, r=8 mm drdt=-1mm/month

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A:

Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

A:

Q: In a certain rectangle, the length of one side is always two inches more than four times the length…

A:

Q: In a certain rectangle, the length of one side is always two inches more than four times the length…

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: The given function of production cost is To find average rate of change of total cost ,use formula

Q: Two straight roads intersect at right angles. A car is traveling south toward the intersection while…

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: (4) If the population of bacteria in a certain region triples in 50 days. In how many days will be…

A: Assuming the rate of increase is proportional to the number of inhabitants. To find- No. of days in…

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: Suppose that the cost of producing x items is C(x) = .005x3 - .5x2 + 28x + 300 dollars, and daily…

A: Cx=0.005x3-0.5x2+28x+300 a). The extra cost of increasing daily production from 50 to 51 items is,…

Q: 2. The population of a certain state is known to grow at a rate proportional to the number of people…

A: 2) Given:         Rate of increase of the population of the state is proportional to the number of…

Q: 3. Imagine you fill your bathtub up at a rate of 2 gallons per minute. This means that every minute…

A:

Q: snip

A: The average rate of change is the slope of the linear function or it can be said that it is the…

Q: 2. The popu lation of certain country is known to increase as a rate proportional to the number of…

A:

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

Q: Suppose a product has a daily marginal revenue of 46 dollars per unit, and a daily marginal cost of…

A: Given,  Marginal Cost, MC = 30 + 1/2x marginal Revenue, MR = $46 Daily Fixed Cost = $200

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: Suppose that the online retailer Amazon needs to use larger and larger cardboard boxes over time.…

A: It is given that, the volume increases by 80 cubic inches each year and  height increases by 0.5…

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Let ,              b → base                      h →attritude . Area of the triangle A (r) = 12bh⇒ b…

Q: Suppose that a product currently sells for $25, with the price increasing at the rate of $2 per…

A: Given, Currently products sells for $ 25  and at this price consumers will buy 150 thousand items.…

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A:

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 41 km/h…

A: Given problem is : Two cars are headed for the intersection of the two roads. If Car A is travelling…

Q: radius of a right circular cylinder is increasing at the rate of 10 in/sec , while the height is…

A: Given query is to find the rate of change of volume.

Q: 4. Mauritius island is 2 km due south of its closest point along a straight coastline. Gibril is…

A: Given data:-

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

Q: Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

A: Given: stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

Q: If in the year 2000 there were 1.26 million metric tons of beef produced and demand is growing at a…

A:

Q: (4) If the population of bacteria in a certain region triples in 15 days. In how many days will be…

A: Bacteria increases proportional during the period given in the problem

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches

A:

Q: 2) What sets linear functions apart from all other equations and graphs is that the average rate of…

A: The objective is to interpret the AROC and slope of a linear function.

Q: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of…

A: Given: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the…

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: In a certain rectangle, the length of one side is always two inches more than four times the length…

A: Given query is to find the rate of change area.

Q: 4. One bucket starts at noon with two liters of water, and water is gradually leaking out at a rate…

A: As per our guidelines I am solving only first problem please repost other question.     For first…

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: The price of a share of a company's stock has been decreasing at a constant rate of$0.50 per share…

A: The price of a share of a company's stock has been decreasing at a constant rate of$0.50 per share…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…