2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y²-3x² and the ry- plane. (Hint: Use trigonometric substitution to evaluate the formulated double integral.)

Q: Let a₁ = a₁ = a₂ = 2 and an = an-1 + an-2 + an-3 for n > 3. Prove, using strong ao mathematical…

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Q: Find a parameterization of the cap cut from the sphere x² + y² +2²=25 by the cone z = √√x² + y².…

A: Solution :  Options (B) is correct

Q: H:3: Expand the following function into its Fourier series : f(t) = cost & te [-π, π]

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Q: 4 Find the general Solution of the following PDES -X • 3 Ux + 2 Uy =o UCX, O) =4e 2 (3y-2x)/2 ans-…

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Q: 6 By separation of variables, Solve the following 5 PDES :- du dt = 2 d24 dx2 © o U (0₂t) =(4,t) U…

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Q: 6 By Separation of variables, Solve the following 5 PDES :- d²4 d24 dx² 0 o u(e,t) = u(s, t) =6…

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Q: 1 Function on the interval (-3,3) and has n=5. Draw the graph. 2 x +1 Determine the approximate area…

A: By trapezoidal rule .∫abfxdx= Δx2​fx0 +2fx1+2fx2+2fx3+⋯+2fxn-1+fxn       where    Δx=b-an    By…

Q: 6. A rectangular classroom has length that is 1 meter more than 2 times the width. Find the…

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Q: if f ofen mapp Prove that for every. xeX and for every ofen Set Vxe Tx in x contains the Point x…

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Q: Which one of the following data is an interval data?   a Typhoon signal     b Student number…

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Q: Set up but do not evaluate an integral that represents the volume of the solid of revolution 2x + 1…

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Q: classify the following PDES :- 227 дх2 -2 822 буду +2 82 дуг =X+3y 2 2 X ох Ихх - 2ху Иху +у Иуу e

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Q: old per ey as a ed an ins

A: This is a problem related to insurance calculation. Based on the policy of the insurance and concept…

Q: Which one of the following is a proposition/statement? a) Is 20 an even number? b) Six is not a…

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Q: Find the particular solution to the differential equation: 2(y')² ( y" = 1- when +3) x = 0, y = 1…

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Q: Problem 1. Consider a periodic square wave defined by -T/2<t<T/2 by y(t) = -1,-T/2 < t <0 1,0 < t <…

A: Solution:Square wave is defined as :y(t)=-1, -T/2&lt;t&lt;01, 0&lt;t&lt;T/20, at t=T/2 and 0Clearly…

Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: By direct partial integration, Solve the following PDES 8- X 8²Z 5 4 dz z(x,0) =X+X, Z (2,y) = 3 y z…

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Q: 4. Check whether the following transformation is an isomorphism from M₂2 to R4 a [a b] a+b a+b+c ]…

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Q: 5 By Separation of variables, Solve the following PDES :- ²4 ● ²4 dx² t>o dt² 0 < x <5 u(e,t) = u(s,…

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Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

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

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Q: Determine the critical (equilibrium) points. dt First enter the smallest value, last enter the…

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Q: Partial Differential Equations Tutorial sheet classify the following PDES :- 227 822 827 ● +2 =x+3y…

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Q: 2. A man put a pair of rabbits in a cage. During the first month the rabbits produced no offspring…

A: It is given that during the first month the rabbits produce no offspring and thereafter produced one…

Q: 17. Ancient pyramid The Pyramid of the Moon at Teotihuacán in Mexico has a rectangular base. The…

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Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: aluate

A: The limit of integration of the variable x varies from x=y13 to x=2. The limit of integration of the…

Q: D. Suppose p, q, r, s are propositions such that p^q is true and rv sis false. Determine the truth…

A: We know that,  A∧B is true if and only if both A and B true  A∨B is false if and only if both A and…

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: Function g is graphed. ← 9 -4 -3 -2 -1 Find [9(z) dar. g(x) L' g(x) dx = 4 3 2 Y H + -1 -2- -3- -4 →…

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Q: What is the probability that a positive integer selected at random from the set of positive integers…

A: Given:   What is the probability that a positive integer selected at random from the set of positive…

Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: 1. Use de Moivre's theorem to find all solution to 25 +32 i = 0. Give the solutions in polar form…

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Q: Show that (2+x, e) is linearly independent. Plz solve both parts within 30-40 mins I'll upvote your…

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Q: 20x₁ + 15x₂ + 10x3 = 45 -3x₁ -2.249x₂ + 7x3 = 1.751 5x₁ + x2 3x3 = 9 -

A: Given system is 20x1+15x2+10x3=45-3x1-2.249x2+7x3=1.7515x1+x2-x3=9

Q: A. A television (TV) set is for sale at P13,499 in cash or on installment terms, P2,500 each month…

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Q: the area bounded by the parabola y ² =4ax, the y-axis, and the line y=2a revolves about the line…

A: given that the region is bounded byy2=4ax and y=2a and  revolves about y=2a Graphically,

Q: A linear operator T: P2 P2 is defined as T(p(x)) = p(2x+1), i.e. T(c + c₁x + c₂x²) = C₁ + c₁ (2x +…

A: Here T is given linear operator from P2 to P2. First we have to find matrix TB of T with respect to…

Q: 8. A frog is at the bottom of a ten feet well. Each day it crawls 2 feet and loses its grip and…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of X dv 2x dv ду = V ax

A: A partial differential equation is an equation containing more than one independent variable, one…

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: using Mathematica]

A: To prove that            ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1, y1 and x2, y2.

Q: Answer the following: 1. Find the inverse of A = - 1 23 using the Gauss-Jordan method.

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Q: Start with an unknown number. Triple it and then subtract 5. Now, take the new number and double it…

A: Let the original unknown number be x. Triple it and then subtract 5 :   3x-5 Take the new number and…

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: no of edges for a tree with number of vertices 10 is

A: Given : Given that the tree with 10 vertices To find: To find no. Of edges

Q: 3. Integrate f 10(x+6) x² + 3x-10 2 dx by using partial fraction.

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Q: Does the following series converge or diverge? Σ 4√n 10n3/2 +7n+7 n=1 The series diverges. The…

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Q: 55² +25-4 (5+₁) (S+₂) (S+ 3) Taking Laplace transform

A: First do partial fraction then find inverse Laplace transform by using standard formulas as in next…