Prove by contradiction that if a sum of three real numbers is less than 30, th at least one of the numbers is less than 10.

Q: 1. Let f : Z6 → Z6 be such that f(7) = x² + 3. %3D (a) Is f a well defined function? (b) Is f…

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Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

Q: For problems 4 - 6, evaluate I= -dz on the given contours. Question #4) Question #5) Question #6)…

A: We have to evaluate I = ∮C 1z4 - 1 dz on the given contours :          4.   C4 : z - 3 = 3…

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This is a problem of Differential Geometry.

Q: The​ O'Connors own a small janitorial service. John requires 14 hour more time to clean the Moose…

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Q: 3. Let f(r, y) = Isin ry. Find: (a) fa(1,9) (b) fy(1, y) (c) fyy(I, y) (d) fyz(I, y)

A: To find  Partial derivatives of the given function.

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim f (x)= 21 b) lim x-x+1=-5 x3 c) limx =8 x→2

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Q: Evaluate sin z dA, where A is the same triangle as in the problem above.

A: The given double integral is: ∫∫Asin xx dA where A is the triangle bounded by x-axis, the line y=x…

Q: luate Sa F . = 3x² i + (=

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Q: Az + 2xy²)dx + (cos y + 2x²y)dy = 0

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Q: hw.2 Evatuate the fotawing cartesian integrats by changing theminte equivalent Pala integrals: dy dx

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Q: IV. Graph each of the equations: 10. x+ 2y = 4 11. y = 2x – 3 12. x = 5

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Q: sin x – e-* = 0, [0,1]

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is…

Q: (2xy + 6x)dx + (x² + 4y*)dy = 0

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Q: Evaluate the iterated integral:

A: It is known that ∫xndx=xn+1n+1+C.

Q: Find local extrema implict function f(x,y) = x*y given condition

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Q: 2z2 - z+1 3. Evaluate J.E- 1)2(z+1) dz for T below. |

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Q: 1. Find the DIFFERENCE between Matrices H and E. That is: [H] – [E]. Name it, "Matrix I". 2. AUGMENT…

A: (a) find the difference between matrices H and E given…

Q: (x + y)dx – xdy = 0 With the initial condition that y=1 and when x =1. A.) Approximate the value of…

A: This is a problem of Numerical Analysis.

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: Q1/ Graph the following functions (choose 2 only) 1) y = 4 sin x 2) y = cot x 3) y = csc x

A: (1) Calculate a table of points for y=4sinx taking the values of x as 0, π2, π, 3π2, 2π. x y 0…

Q: Problem 3 Use Lagrange multipliers to find the dimensions (in meters) of a rectangle with perimeter…

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Q: II. Solve each equation by completing the square: 4. x2 + 12x – 2 = 0 5. x(x – 1) = 30 6. 2y? + 7y –…

A: Solving Quadratic Equations usingCompleting the Square we follow the step given below : 1. Divide…

Q: 6. ints) Let V be a vector space of dimension n and W a vector space of dimension m. Let L: V- W be…

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Q: SET-UP the double integral that solves for the volume of the solid:

A: To find the volume of the solid using double integral of the region bounded by below surfaces in the…

Q: Describe the graph of the equation: r = 4ti – 5j + (1 + 2r)k. [Choose the correct answer.] O The…

A: Introduction: In three dimensional Euclidean space, a line can also be represented. An equation of a…

Q: Q Final the complement f the gwaphs in fig-1-34 figti3t

A: We have to find the complement of given graph.

Q: In questions 2, 3, and 4, consider the following biobjective linear pro- gram (BOLP): – x2, f2(x) =…

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Q: f(t) = e-4(t-cos(t))

A: We will use laplace transformation properties and table to find value of laplace transformation and…

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: For an n × n matrix A, we can similarly define the matrix exponential aseA = I + A + (1/2!)A^2 +…

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Q: Find the volume of the pyramid with base in the plane z = -9 and sides formed by the three planes y…

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Q: The slope of the surface z ry in the r-direction at the point (2,3) is. slope of this surface in the…

A: The slope of the surface z=xy2 in the x direction at the point (2,3) is =∂Z∂x2,3 . Now ∂z∂x = y2.…

Q: Figure Q2 shows an 11 m long steel beam AC of uniform cross-section, simply supported at left end A…

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Q: Evaluate F(2). f(t)=sin(2t)sin(3t) round-off to 4 decimal places Answer: 0.1655

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Q: Problem 4. For the matrix A find all eigenvalues and all eigenvectors. Determine an algebraic and…

A: Given A=4-234 We will find all the eigenvalues and eigenvectors.

Q: Q3. Solve the following LP problem using the simplex method: Maximize: Z- 2x + y Subject to: 2x +…

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Q: a) Find the matrix A. Hint: A = PDP!, Note: you don't need to know A for the rest of this problem.…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: f a baseball player has a batting average of 0.255​, what is the probability that the player will…

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Q: Aayush and Abbey have the following system of differential equations da dt -5 x + 12 y dy = -2 x + 5…

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Q: Q2) Find the optimal solution using simplex method Max z = 8x, + 10x, + 7x3 s.t: 4x, + 6x2 + 3x3 5…

A: The problem is max z=8x1+10x2+7x3 subject to 4x1+6x2+3x3≤607x1+2x2+5x3≤406x1+6x2+9x3≤36…

Q: 3. LetR be the region shown in the accompanying figure. Fill in the missing limits of integration.…

A: (a)  ∫∫Rf(x,y)dA=∫24∫13f(x,y)dydx + ∫45∫2x-73f(x,y)dydx

Q: Write the equation in standard form of the circle whose center is at (0, 0) and that is tangent to x…

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Q: the of olution using simplex me Max z = 8x, + 10x, + 7x3 s.t: 4x + 6x3 + 3x3 S 60 7x, + 2xz + 5x, S…

A: In this question, the concept of Linear Programming is applied. Simplex Method An approach to…

Q: A spherical tank of radius 4m is filled with water to a height of 1.2 m. The water is transferred to…

A: Let us find the height of the frustum of the cone in the next steps.

Q: (2.x + x²y³)dx• + (x*y² + 4y³)dy = 0

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Q: SET-UP the double integral that solves for the volume of the solid

A: To set up a double integral to find the volume of the solid.

Q: 4. Evaluate the iterated integral: dydr.

A: To Evaluate:∫141∫x2xxydydx

Q: e of z cos (÷) a

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Q: 1. Find the maximum value of r+y subject to the constraint r + y? = 18.

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