The total revenue function for a commodity is given by: R(x) = 80x-0.04x2 A) Find the marginal function revenue B) What is the marginal revenue when x = 100? C) Interpret your answer in part B.

Q: A steel ball weighing 2 lb is dropped from a height of 3000 ft with no velocity. As it falls, the…

A: Locate the coordinate system with ground x = 3000 , w = 2lb  , k = 1/8 Assuming g is 32 ft/s W =…

Q: The side of an equilateral triangle is increasing at a rate of 2 m/sec, then the rate at which its…

A:

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

A:

Q: 20. What is the value of SSy? (SHOW YOUR WORK)

A: For the given data ( 20 ) SSY = ?

Q: The marginal cost of producing the xth box of light bulbs is 4 + dollars per box. Determine how much…

A: Marginal cost= dc/dx=4+ x^2/1000 integrating on both sides will give us how much cost is added by a…

Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

A:

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: The length { of a rectangle is decreasing at a rate of 8 cm/ sec while the width w is increasing at…

A:

Q: Use a linear approximation to estimate v100.5. Show your work.

A:

Q: Find f'(x) using the delta definition of the derivative (i.e., limit process) vhere f(x)= x² – 5x…

A: Given that        f(x) = x2 - 5x + 12 Here we have to find f'(x) by using the delta definition of…

Q: The firm is very interested in maximizing profits. Its profit model is given by the function: f(x) =…

A: Solution is given below:

Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

A:

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: 5. Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick.…

A:

Q: Assume that it costs a company approximately C(x) = 529,000 + 160x + 0.001x2 dollars to manufacture…

A:

Q: What positive number added to its reciprocal gives the minimum sum?

A:

Q: The side of an equilateral triangle is increasing at the rate of 3 cm/s. What is the rate at which…

A: We can solve the given problem by using the following concept of differentiation. Let f(x) be the…

Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

A:

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

Q: If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what…

A: (a)Given:

Q: Find the total derivative of V with respect to X

A: As the differentiation is with respect to x, x becomes the variable. y and z becomes constants

Q: The volume of water in a hemispherical bowl of radius 30cm is given by V =36x2 – x³ ) where x - X cm…

A:

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

Q: The length l of a rectangle is increasing at a rate of 7 cm divided by sec while the width w is…

A: Given:-             The length l of a rectangle is increasing at a rate of 7 cm/ sec while the width…

Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

A:

Q: Assume the learning rate for new skills is proportional to the difference between the maximum…

A: The learning rate for new skills is proportional to the difference between the maximum potential for…

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: 30. Based on the R output, the most appropriate coefficient to describe the relationship between…

A: The R-output of Pearson's correlation and Spearman's correlation is given.

Q: The area of an equilateral triangle is decreasing at a rate of 3 cm^2/min. Find the rate (in…

A: We want to find the rate (in centimeters per minute) at which the length of a side is decreasing…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: The side of an equilateral triangle is increasing at a rate of 3 m/sec, then the rate at which its…

A: Let the side of an equilateral triangle be x cm.∴ Area of equilateral triangle, A = √3/4x2…

Q: Suppose that y is inversly proportional to x. If y = 6 when x = 3, find thd constant of…

A:

Q: If a ball is thrown vertically upward with a velocity of 25 m/s, then its height after t seconds is…

A:

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: The given function is fx=9x2+7. Note that, the denominator of the above function is not 0 for any…

Q: A tank originally contains 385 litres of brine holding 470 N of dissolved salt. Eight litres/min of…

A: We will find out the required solution.

Q: The length { of a rectangle is increasing at a rate of 9 cm/sec while the width w is decreasing at a…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: ㅠ -π sec xdx. 3

A:

Q: Use a linear approximation to estimate V8.05.² Show relevant work to explain your reasoning.

A: Linearization: If y = f(x) is differentiable function at x = a, then linear approximation at the…

Q: A linear density of a rod of length 16 m is given by p(x)=25sqrt x+4 measured in kilograms per…

A:

Q: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a…

A: The derivative is also called the rate of change of a quantity with respect to time. The volume of a…

Q: Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where a and b are…

A: ANSWER :

Q: If a ball is thrown vertically upward with a velocity of 15 m/s, then its height after t seconds is…

A:

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

A: