I. SOLVE the following DIFFERENTIAL EQUATIONS using appropriate method. 1. (x²+6y?)dx- 4xydy3D0 2. (2x - 3y +1)dx- (3x+2y-4)dy 0 3. y'sec'xdx- (1- 2y'tanx)dy 0 4. dx + (x - y + 2)'dy 0

Q: 1. Let X be G-measurable and let Y be independent of G. Let f(x, y) be a bounded continuous function…

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Q: Solve this ODE using the Frobenius Method x²y"+x²y'-2y = 0

A: given ODE x2y''+x2y'-2y=0             ...i solve this ODE using frobenius method

Q: 1 X(z) =; (1– z-')(1– z-²)

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Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Determine the last three digits of 202220232024 + 20072002 + 2019

A: ............ 684 So last three digits is 684

Q: D2) Let A= Fid ABud BA al B.

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Q: O Proof: a Contradiction: V2 is an irrational number O The sum of a rational number and an…

A: Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are…

Q: 3. For each of the following, decide whether there is one solution, no solution or infinitely many…

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Q: You manufacture two types of toys: for boys and girls. Each toy goes through 3 processes: grinding,…

A: We will construct a linear programming problem according to the given conditions. Let x and y is the…

Q: Find the area of the region bounded on the left by x = y? and on the right by x = 3 – y?. O a. 7 sq…

A: Given: Equation of curves  x=y2x=3-y2

Q: Find the solution. dy 2y +==x?y?sinx dx y = x?(sinx-c) B y = x²(cosx+c) (c) y = x²(cosr+c) D y = x (…

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Q: Question 6 Find the solution. dy 2y dx Ay = x(x+c) By = x³(x+c)3 y = x²(x+c)2 Dy = x2(x-c)-2

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Q: The bases are regular hexagons. The area of each is about 41.6 cm^2. Find the sum of their areas.…

A: Given: There are two regular hexagons with sides 4 cm. Concept: Now we shall use the formula,…

Q: In how many ways can an employer select two senior staff from seven candidates, and three junior…

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Q: Q1

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Q: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

Q: Q2: Using the rules, convert the following differe ntial equation into exact, then solve x* ydx-(x'…

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Q: Completed as soon as possible thank u Suppose there is a firm with at least some market power that…

A: Given: A firm with some market power supplies the same product to two markets.

Q: Calculate the area of the region bounded by the curves x = = y² and x-y=2. a. 11/5 sq units O b. 9/2…

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Q: 6. Write the addition and multiplication tables for Z7.

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Q: 3. Use De Moivre's Theorem to solve for the roots of : a® – 1 - jl = 0 O A. 1 cjs (T/24 + TIk) ; k =…

A: To find the nth root of the complex number Z = r [cos(θ) + i sin(θ) ] in polar form, use the formula…

Q: 4. Solve the linear system below a + 2b – c + 4d = 1 —а — 3ь + 2с + 2d %3D 4 2а + 2b — с + 2d %3D 2…

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Q: Find the solution of the following system if (0) = 0 and y(0) = 1. z'(t) = 8x(t) – 3y(t) y (t) =…

A: We have to find the solution of the given system.

Q: dQ 21. t + Q = t*Int dt 22. (2x + y + 1)y' = 1 23. (x2 + 4) dy = (2x – 8xy) dx | 24. (2r cos 0 sin0…

A: Divide both sides of the given equation by t to obtain standard form. tdQdt+Qt=t4lnttdQdt+1tQ=t3lnt…

Q: Find the solution for the system of Linear equations using Gauss-Jordan Elimination of the augmented…

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Q: Find the general solution of the equation: y" - y' - 6y = exp(-x) - 7 cos x %3D

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Q: 3. For a metric space (X, d), the diameter of a subset A C X is defined by 6(A) := sup d(x, y).…

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Q: Find the absalute maxima and minima for the function 48xy -32 x 4 yen thhe rectangulaK plate boundad…

A: We have to find the absolute maxima and minima of f(x,y).

Q: 5. Compute sin a e + 3e¬z

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Q: By using Laplace transform to solve y"-y e' with y (0) = 1 and y (0) = 0 ,what would the particular…

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Q: How.L Find minima, bmakima and Saddle paints for the functionss foxy) -9x -4 xy 3- %3D f Cx,y) = 2…

A: (3) the given function is fx,y=9x3+y33-4xy Now we have to find ∂f∂x,∂f∂y,∂2f∂x2,∂2f∂y2 and ∂2f∂x∂y

Q: Calculate the inverse: s2 +1 L-1 (s – 1)(s + 1)(s – 2)J

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: If my recipe calls for 65 lbs of cubed sweet potato, and it has a yield of 75%, how many whole…

A: Given, recipe calls for 65 lbs of cubed sweet potato, with a yield of 75% .

Q: Question 11 Find the solution, (D3+3D²+3D+1)y = 0 (A y = (c,+c,r+cx?)e= © y = c,e"+c,„xe -3«. Oy =…

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Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: Given: Min Z=600,000x+500,000y 300x+100y>900 200x+100y>800 150x+150y>750 Solve for z

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Q: Uindaterraind coefdicients y" t 4ytuy = (3+x)e"; yro)=2, y'6) =5 %3D

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Q: Find the volume of the solid generated when the area bounded by the curve y = vx, the y-axis, and…

A: Volume is the measure of the amount of space occupied by a closed surface. It is measured in terms…

Q: (1) Consider the following differential equation, with time domain t e (0, 1): Sv = (-1)y. u(0) = 1.…

A: The complete solution is in given below.

Q: If and i are independent co-ordinates of a point, show that = &

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: As an easy exercise, check that you believe that lim [0, 1- 1/n] = [0, 1) %3D lim [0, 1- 1/n) = [0,…

A: limit is that value of function at which function approaches to output at any given input. The…

Q: 3. Kenny wants to invest $ 250 every three months at 5.2% a compounded quarterly. He would like to…

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Q: For each statement below, indicate whether the statement is true or false. (a) mal solution or…

A: (a) we know that if in the dual simplex method there doesn't exist the optimal solution then the…

Q: Write down the augmented matrix corresponding to the following system of equations in five…

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Q: Consider a linear system whose augmented matrix is of the form 11 32 1 2 43 13 mn For what values of…

A: The given problem is to find that for what values of m and n, the given linear system in augmented…

Q: Solve for the following to find the inverse laplace transform.

A: Introduction: Laplace transformation in of the most important integral transformations that…

Q: Find the centroid of the region bounded by the graphs of the functions y = 4 sin(x), y = 1 and x =…

A: We can find the centroid by using formula

Q: 3S+8 2)

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