For Exercises -41 solve the IVP. Sx², x <1 where y" (1) = e +, y'(1) = e + and y(1) = e + 59 81 41. y" – 4y" + 3y' = 1, x > 1 27

Q: Find the mass of a plate bounded by one arch of the curve y = sin x, and the x-axis, if the density…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: 4. Find the volume of the solid generated by revolving the first quadrant area of the curves xy=2,…

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Q: Sketch the graph of f(x) = 2Vx + Vx*.

A: Graph of f(x) :

Q: Find the equation of the circle of curvature of the curve y= 2x" –x' at its minimum point in the…

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Q: (b) Calculate sin(arccos()) exactly, i.e. without using a calculator.

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Q: 4) golve the luP : ty"-24'+ty = t Chne 'a ) yro) = |

A: Solution: given, ty''-2y'+ty=t  y(0)=1, y'(0)=0 it is a non homogeneous equation so solution will be…

Q: 4: Solve the following differential equation using Laplace transform 1. y y, +3yz, y = 4y, - 4e y(0)…

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Q: Use only the Stokes’ theorem to evaluate  integralC(−z − y)dx + (x − z)dy + (x − y)dz where C is the…

A: Solution: given  F=-z-y,x-z,x-yand C is the intersection of ; z=x2+y2 and z=y First, we solve the…

Q: a) RDL Corporation has one small plant located on the outskirts of Manila. Its production is limited…

A: First, we have to set up the linear programming model. Then, we can proceed further.

Q: f(x) = x* +16

A: Solution :-

Q: QUESTION 1 Given the first order differential equation dt dy 2y2 +t? 2yt find the general solution…

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Q: Problem 2: 2.5 Evaluate the integral using the composite trapezoidal rule with the indicated number…

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Q: Determine the exact solution of the following differential equation y = 2 - y at y(0) =1 So the…

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Q: 8. (a) Let I = :| f(x) dr where f(x) = 7.x +2 – V7x + 2. Use Simpson's rule with four strips to…

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Q: 1 0 -2 -4 -6 е. 0 1 X = -8 6 10 0 0 -6 8 -9 X = 0 0 1 -7 -2 -10 f. 1 X 9. 1

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Q: non-neza tive intezer solations of X, +Xa+Xg + X4+ X6tX= 30 2. Consider as How mony di Staent…

A: Explanation : x1+x2+x3+x4+x5+x6=30 problem can be understand by that we have to distribute 30 items…

Q: Prove the statements: The difference of the squares of any two consecutive integers is odd.

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Q: TRUE OR FALSE 7. When proving, the proposition that needs to be shown may be used as a…

A: 7 False 8 True

Q: Let G, and G, be two groups. Let H and H, be normal subgroups of G G, respectively then @ H, x H, 4G…

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Q: The time (in minutes) between arrivals of customers to a post office is to be modelled by the…

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Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: Advanced Math Determine alln >0 such that the decimal expansion of 1/n has period 1.

A: case1: let the decimal expansion of 1n has period 1 after 0 non repeating decinmals: 1n=0.d1d1d1....…

Q: Find the common area betuween V=2C1+Cose) and carved V=2(1-Sine) which is Locatel in the Fuorth…

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Q: 1. Solve the linear system using Jacobi and Gauss-Seidel Method 2x – y = 2 3y + z = -2 - -x + y – 3z…

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Q: Let V be a finite dimensional inner product space. Then the set of all orthogonal transformation o n…

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Q: Hiwg Solve U tt= 16 Uxx h= k cat) = U (5,t)20 u (5,t). u(X, o)= X (5-X

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Q: Determine the area of the region below. A. 1.5 sq. units B. 1/2 sq. units C. 1 sq. unit D. A sq.…

A: Solution

Q: Problem 6. Let X be a normed space. (a) Find all subspaces of X which are contained in some ball…

A: We will use the basic knowledge of functional analysis to answer both the parts of this question…

Q: An experiment consists of three fair, different coloured dice being rolled (the dice are 6-sided and…

A: Given that A is the event that none of the dice shows 1. To find: (a) the sample size S.…

Q: A man gets to maintain his body temperature. How much fat should he burn if he needs to do 350 000 J…

A: Given: A man gets to maintain his body temperature.   To determine: The amount of fat that he should…

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: 2. Using Gaussian Elimination a.3x + y - z = 1 b.x - у+z%3D-3 c.2x + y +z= 0

A: Solution :-

Q: 6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

A: We have to solve given Questions.

Q: Q3) Solve the following boundary value problem using finite difference method dy +2y = 0 dx y(3)=…

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Q: Calculate the formal asymptotic expansion of the initial value problem x' = -ɛx +1, x(0) = 0. up to…

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Q: 1. Use the Diagonal Method to evaluate the value of the determinant: 3 4 2 -1 – 3 1 - 2 2 3 -1 1 2…

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Q: What is the sketch the phrase "three collinear points and a fourth point not on the line of the…

A: We will use the basic knowledge of geometry to answer both the subparts of this question completely…

Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + %3D subject to 2² +…

A: Let function F(x,y,z) subject to constrant g(x,y,z)=k Lagrangian L is L(x,y,z,λ)=f(x,y,z)-λ.g(x,y,z)…

Q: Determine if each function is injective, surjective or bijective. Give one counterexample for each…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: Given function: hx,y=x3-3x+3xy2 To find: all the relative minimum and maximum values, and saddle…

Q: An experiment consists of three fair, different coloured dice being rolled (the dice are 6-sided and…

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Q: Q4: Solve the following differential equation using Laplace transform 1. y' = y1 + 3y2, y2 (0) = 1…

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Q: 6. A home improvement company expects to sell 180 kitchen sinks during the year. There is a $60…

A: Suppose that the company order x sinks in each shipment. then on an average there would be 12x sinks…

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: Find all the Laurent series representations of the function f(z) = 1/(z − 3)z centered at 0.

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: The given function is hx,y=x3-3x+3xy2...(1) To find: The maximum, minimum values and saddle points.

Q: A jet plane is flying west at 5 feet per sec at an altitude of 4000 feet. The plane is in vertical…

A: Solution:-

Q: 3. Show that sin? z + cos² z = 1, 2 € C, assuming the corre sponding identity for : €R and using the…

A: Solution for 3:  Prove that: cos2z+sin2z=1; let, for acute angle z   now,take LHS =cos2z+sin2z

Q: ) Perform the Gram-Schmidt orthogonalization process for u = x + 1, u2 = x2 + 3, u3 %3D Va using the…

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Q: 10. G(t) = t5 –e-9t + 5(t – 1)2 4 16-

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