A cylindrical can of height h and radius r is to be made with a fixed volume V. Show that the area of material used is minimised when h = 2r.

Q: b) Find the area between the 2 curves f(x) = x² +4-4x and x- with the two lines = 5 &x= 2. axes and…

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Q: 8 {4} {{ {}₁ s² + a² s² +6² (1)

A: We have to find the value of a+b.

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: -3x + 5z x + 2y = 1 - 4z-7y=3 -2=0

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Q: 1. Approximate the area under the graph of ƒ(x) = x² + 1 from x = −1 to x = 2. a. Sketch the graph…

A: We have to approximate the area using Riemann sum.

Q: Q5(a) Let f(x) be a periodic function with period 4 such that f(x) = {2; 0<x<2 2<x<4 (1) Find the…

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Q: Find the general solution of this ODE: d²y dt² +13- +36y 4t² - 6+10e-2t dy dt = The solution will be…

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Q: rt - fe e2u f(u)du f(u)dut-

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Q: Evaluate the double integral: LLantes x² +1 yl/3 (Hint: Change the order of integration to dy dr.)…

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Q: The diagram shows the curve y = ex and the tangent drawn at x = 2. AY X

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

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Q: Problem 1. Consider the differential equation dy 2x²+2 = dx X where y = 5 at x = 1. Use RK4 Method…

A: consider a differential equation dydx=2x2+2x with initial condition y1=5 use RK4 method to determine…

Q: 4. Use Cartesian coordinates to set up the iterated double integral given by Iff v² av D where D is…

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Q: By direct partial integration, Solve the following PDES 8- • Xd²z ахду dz ду + =0 Z(X,0) = X+X =X+X,…

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Q: 0 What is/are the correct explicit definition for {an} = 1, 2 3' 97 27... (choose all that applies)…

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Q: Use mathematical induction to prove that for all integers n ≥ 1, 1 +7 +13 + 19 + ... + (6n − 5) =…

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Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

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Q: Find the Laplace transform L (cosht cos²t) @ & L (sinhst cashet) (2 3 L (sin't cos't)

A: Here we use the conversion of hyperbolic function to exponential function. And use some…

Q: • Find the upper Riemann sum U(f, P) and the lower Riemann sum L(f, P) for each of the following…

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Q: (d) The set {(x, y) = R² | y 0} is empty. ( ) (e) If A is a subset of B, and B is a subset of C,…

A: According to our guidelines we can do at most three sub-part of a question at a time. So please post…

Q: F :1: Solve L-1)2(s+10)-140 섹 (s+1)² +400)

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Q: Let M, be the additive group of all nxn matrices with real entries, and let R be the additive group…

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Q: A mass of 1.25 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous…

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Q: 4. Solve the following 2nd-order OPES (5 Steps) day - (22) + (4-1) dy dx² Y(0) = 4 , y(0) = 1 y cas…

A: We can solve this using euler method of second order differential equation

Q: What is the negation of the proposition/statement: 9 14                                  b) 9 ≥ 14…

A: Solution :  Options (B) is correct

Q: 5.S) A spring with a 8-kg mass and a damping constant 11 can be held stretched 1.5 meters beyond its…

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Q: x - 1 5 = y - 2 3 Z - 2 1 2xy +z = 10

A: To find the solution of a system of equation is the values of the unknown for which the system of…

Q: 14. Find the cube root of 15 correct to four significant digits by Fixed-Point and Secant methods.…

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Q: Evaluate the double integral that will find the volume of a solid bounded by z=1-2y²-3x² and the…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: Consider the differential equation " - 4y + 5y = f(t). such that y(0)=0 y y'(0)-2. The function f(t)…

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Q: m For fixed a, consider the quantity cos(x + h) Q(x, h) = a) What is the limit (x) of Q(x, h) as…

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Q: Find the general Solution of the following PDES • 3 Их + 2 Иу SO > u(x,c) = чех (3У-2х)12 ans3-…

A: Given partial differential equations are , (.)    3ux+2uy = 0   ;    u(x,0) = 4e-x (.)…

Q: Obtain the circulation integral of the field F = xyî + y²ĵ in the curve C defined by the boundary of…

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Q: Q5: Use the quadratic interpolation and the following data to find f(1.4) X 1 1.2 1.3 F(x) 0.368…

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Q: Use the Sequential Criterion for Integrability to show that if f: IR is Riemann integrable on I =…

A: The main objective is to prove that if f is Riemann integrable then cf also Riemann integrable.

Q: Solve the following differential equations : X 2y + v² 2x (x² + 5)² dx + (x+y)dy = 0

A: First we will check if the given differential equation is exactly if it is not exactly then we will…

Q: 3 By direct partial integration, Solve the following PDES 8- J 8²u axdy 2 = cosx cosy, x4(X₂ #) =X U…

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Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: Solve the following system 2x₁6x₂x3 = -38 -3x₁ - x₂ + 7x3 = 34 -8x1 + x₂ - 2x3 = 20 using the Jacobi…

A: Given system is 2x1-6x2-x3=-38-3x1-x2+7x3=34-8x1+x2-2x3=20 We can write it as x1=-1820-x2+2x3…

Q: 3. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money,…

A: Let assume  $x he start with the first week One week he tripled his money = 3x But he lost $12 Left…

Q: 2. Let f I→ R be Riemann integrable on I = [a, b], a, b = R, a <b, and let F be an an- tiderivative…

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Q: 16. Measurement Given the perimeter, P, and the lengths of two sides of the triangle, find the…

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Q: 4. Solve the following 2nd_order OPES (5 steps) day = ( x ) = + (1 - 1) dy dx² dx h=0.02 Y(0) = 4 ال

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Q: Use the Jacobi method to find approximate solutions to 3x110x2 - 4x3 = 9 20x1 + 2x2 + 3x3 = 25 2x12…

A: Don't confuse with the notation of variable . Here we use xk,yk,zk for approximate first ,second…

Q: An internet job recruitment company, Company1, claims on their company doubles the probability of…

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Q: wer contain e drawer c x, one draw

A: Given information: There are 3 boxes and 6 drawers in them. Each box contains two drawers where…

Q: = Solve the recurrence relation an 7an-1 12an-2 for all integers n ≥ 2, a₁ = 1 and a₁ = 6.

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Q: 5. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.…