2. The weekly revenue of a newly released film is given by 15t R(t) for t 20, 2+ 10' where R is measured in millions of dollars and t is in weeks. (a) Find the critical points for this function. (b) For how many weeks will the weekly revenue be increasing? (c) What is the maximum weekly revenue?

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x? + 6x +…

A: Given function is as below : C(x)=2x2+6x+12 Marginal cost can be given by Derivative of C(x) .…

Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

Q: The approximate value of y(3) for the initial value problem for ' = cost + sint, y (0)=0.5 with h=…

A: Correct option is (b) 2.631 Detailed solution : Given y′=cos(t)+sin(t),y(0)=0.5,h=0.5,y(3)=?Forth…

Q: Suppose f(x, y) = x² + y² – 2x – 8y +1 (A) How many critical points does f have in R? ? (B) If there…

A:

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: Find the number of units x that produces the minimum average cost per unit C (with a line over the…

A: We have to Find the number of units x that produces the minimum average cost per unit C (with a line…

Q: juice company has found that the marginal cost

A:

Q: The productivity of a country is given by f(x,y) = 100x0.6°y0.37, where x is the amount of labor and…

A:

Q: Use implicit differentiation to find dy dx when x = 1 if x + xy + y2 = x3y2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference…

A: This question is about application of numbers theory

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4

A: dxdt(3t4+4t2+1)=23=>dx=23dt3t4+4t2+1=>dx=23dt(t2+1)(3t2+1)=>dx=23…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, ß are positive…

A:

Q: Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2?2 + 6? +…

A: Given, Total cost of manufacturing x units of a certain commodity =  C(x) =  2x2 + 6x + 12 We need…

Q: #18 & #19

A: 18. Area under the graph is the integral of the function over the given interval.

Q: 5. Suppose that we have designed a cylindrical storage of radius 6 m and height 10 m, and we are…

A:

Q: The output at a certain factory is Q(x, y) = 7x' + 4x/x e36 + 5y. where x and y denote,…

A: We’ll answer the first question since we answer only one question at a time. Please submit a new…

Q: 9. The average revenue function of x units of product is R(x)=-mx+n,where m and n are constants. a)…

A: Given that: Average revenue function, R¯(x)=-mx+n

Q: A manufacturer has discovered that if x units of a certain item are produced per week, the marginal…

A: To find: The maximum weekly profit that can be made by producing x units of that item. Given…

Q: (d) The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given…

A: Given that : Marginal Cost Function is : dCdx=-0.02x+6. We can achieve Total cost function by…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

A:

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive…

A:

Q: a cost function is given by c(x)=200e^-0.5x. Calculate teh marginal cost when x=3

A:

Q: A manufacturer incurs the following costs in producing x water ski vests in one​ day, for 0<x<200​:…

A: =&gt;c(x)=0.05x^2+15x+245 =&gt;c(x)=0.05x+15+245/x

Q: 1- Find the average rate of change for y == Xo = 1 X1 = 2 2- Find the instantaneous rare of change…

A: Application of derivatives

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: Suppose that the amount of energy (x, y, z) emanating from a source at (0, 0, 0) is inversely…

A: a)  The energy function is proportional to z And, it is inversely proportional to 11+x2+y2    So,…

Q: Apply Euler's method with successively smaller step sizes on the interval [0, 2] to verify…

A:

Q: A manufacturer's marginal-cost function is dc = 0.2q + 5. If c is in dollars, determine the cost…

A: Given marginal cost function is: dcdq=0.2q+5 Where c is cost in dollars and q is production. The…

Q: Suppose that the marginal propensity to save is ds = 0.3 - dy (in billions of dollars) V 9y + 6 and…

A:

Q: C' (x) = 20 200

A:

Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

A:

Q: Assume that it costs Apple approximately C(x) = 36,100 + 100x + 0.01x² dollars to manufacture x 32GB…

A: We use second derivative test to find out where cost is minimum

Q: V Solve usıng variaton of parameters or reduction of order (D²+1) y = tan

A:

Q: 4-5

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: The Strikers Technologies Company determines that the marginal cost for their MaxiPak flash disks is…

A: The Strikers Technologies Company determines that the marginal cost for their MaxiPak flash disks is…

Q: which 20 grams of salt is dissolved. Pure water is being pumped into the tank at a rate of 5…

A:

Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

Q: Find the points at which y=f(x)=x^9−17x has a global maximum and minimum on the interval 0≤x≤4.…

A: To determine the global maximum and minimum.

Q: A company determines that its marginal revenue, R', of selling the xth unit of its product is given…

A:

Q: 12. Find the profit function for the given marginal profit and initial condition. dP = -40x + 290,…

A: Solve the following

Q: Answer all of the following questions. 1.) Find the equation of the line tangent to f(x) = 6 ln(7–…

A:

Q: A company finds that its marginal revenue from the sale of the xth unit of its product is given by…

A: Solve  for total revenue function

Q: At a point where y' = 0, if y changes from positive to negative as x increases, Ay is maximum By is…

A: We want to find true option.

Q: Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y=…

A:

Q: A factory selling cell phones has a marginal cost function C'(x)=0.01x^2-3x+229 where x represents…

A:

Q: (a) A manufacturer's marginal revenue function is: * = 25 – q – 0.3q³. If r is in omani rials, find…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.