Commencing with the Cobb-Douglas function below: q(K, L) = K¹/4L3/4 Optimize q subject to the constraint 100 = 2K + 4L obtain this maximum using the method of Lagrange multipliers.

Q: A right circular tank of depth 3m and radius of 2m is full of water. Find the work done in pumping…

A: Given: Depth=3mRadius=2m To find: Workdone

Q: The expanded form of the differential operator D(xD - 1) is (A) XD²-1 (в XD²+1 XD² - D XD² D

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Q: From a table inside a room with current temperature of 26 degrees Celsius, a left over Fried Chicken…

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Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: How many years are required for P5,000 to increase to P8,000 if invested at 12% per year compounded…

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Q: Evaluate: lim (1 + 2* + 3* + ... + 99t)¹/x X→∞

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Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

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Q: Evaluate. 2x lim (e²x + 2) 8118

A: The solution is given as

Q: (a) Prove that if m ₹ N, then the function f(x) = xm is continuous on R.

A: We have to prove that, the function f(x) = xm,   m∈ℕ  is continuous on ℝ.

Q: The matrix has eigenvalue > = 3 with an eigenspace of dimension 2. Find a basis for the…

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Q: Evaluate. 1²9 dx 2 + X

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Q: Using Fixed-Point Iteration with an initial value of zero, find a root of the function: f(x) = x³ -…

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Q: S. (22² 2. 2 (2x² – 3x) dx

A: ∫25 2x2-3x Apply the Sum Rule:    ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx =∫252x2dx-∫253xdx

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

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Q: Topic: Root Finding using Fixed-Point Iteration Solve the problems and show the complete solution.…

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Q: The particular solution of (D³-5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 1 √√√x+x Solve the integral: S ® h1+x+c A C Gin|5+x²³| +c (B) : C © Bhl1+xel c C) + C 5 5 D) -n|1+x'…

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Q: Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean…

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Q: Initially 56 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

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Q: Find a general solution. 7y" + 13y' - 2y = 0 y(t) =

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Q: Solve the following by Repeated root Method Question 4 X³+ 5x² + 7x-3 = 0

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Q: For the function f(x, y) = 4x³x² + 6x - 7, find the solution from x = 0 to x = 2 with an increment…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: ★ Use the Integral Test to evaluate the series for convergence. ∞ 1 In(In(n))2. n=2

A: Solution

Q: Find the z-transform of the following equations: a. 2un+n b. cos(3n) + 2 sin(3n)

A: According to our guidelines I can answer only question no. (a)

Q: (D² + 1)y = sec² x csc x

A: Solve the differential equation by the method of variation of parameters : D2+1y=sec2xcscx

Q: Exercise 15.2.8 Y 1₁² Find ► Hint dA where D = {(x, y) : x ≥ 0, y ≥ 0, x² + y² ≤ 1}.

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Q: Use a double integral to find the area of the region. One loop of the rose r = 5 cos(30)

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Q: on 3. Let f(x) = |x| Compute f(n) for all

A: Given:  f(x)=x x∈-π,π. To find: a) f(n) for all n∈ℤ.              b) ∑n=1∞12n+14 and  ∑n=1∞1n4

Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 43л A -unit3 135 83л B 135 43л Ⓒ 125…

A: Solution:-

Q: Premise 1: He is an action star or he has the support of the administration party . Premise 2: He…

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Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

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Q: N (z−2)²

A: Follow the steps.

Q: Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤…

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Q: What is the radial lines a and ß of the equation r = sin 30 ? α = 0 and в= A B. a = α = 0 and ³= π/3…

A: Solution:-  Options (b) is correct

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the disk method to determine the volume of solid obtained by…

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Q: Setup the iterated double integral that gives the volume of the following solid. Correctly identify…

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Q: Solve: y""(t)- y" (t) + y' (t)- y(t) = H(t); y(0) = 0; y'(0) = y" (0) = 1; where H(t) (t+3,0 ≤ t <1…

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Q: Find the Fourier expansion of th function and dr periods of the

A: Given function: f(x)=x+πif -π&lt;x≤0πif  0&lt;x≤π   To find: Fourier series expansion of given graph…

Q: Solve the following initial value problem over the interval from t = 0 to 2 where y(0) = 1. Display…

A: To Solve: The Initial value problem is dydt=yt3-1.5y , y(0)=1. (i) Analytically. (ii) Using Euler's…

Q: What is the differential equation corresponding to the general solution y² = Cx³? dy A dx-2x = dx 2y…

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Q: A lamp has two light bulbs with an average lifespan of 1400 hours. Assuming we can model the…

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Q: Given the differential equation: dy y dx with initial conditions y = 1 at x = 2.0, produce a…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. On January 1, 2022, Marites deposited P15,000 in a bank that offered 2.5% annual interest…

A: time from 1 jan 2022 to 1 april 2022 = 3months= 0.25 years so we calculate inerest of 3 months…

Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Create a quadratic model for the data shown in the table 1 -1 X Y -1 -1 Oy=0.85x² +0.11 - 1.78…

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Q: Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 14…

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Q: 6. We always prove an argument. 7. If an argument is true then it is valid. 8. Suppose a declarative…

A: Since you have posted a multi subparts question according to guildlines I will solve first…

Q: Message: [-8 59] [19 43] [10 60] [0 25] [-7 81] 1 2 matrix used: -1 3

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Q: df =2f-48 dt dg - f-3g dt

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Q: B/Find the oblique asymptote of the function f(x) -3x²+2 x-1

A: To find The slant asymptote of f(x)