1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides so that the cross-section of the gutter is an isosceles trapezoid. Find the maximum volume of the gutter.

Q: (a) Consider the matrix 4 0 4 7 -5 1 A = 3 -1 2 1 -6 0 (i) Compute the determinant of A. (ii) Using…

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Q: Sol vet he Vol terra integral equationof first kind g(t) g(x-t)dt = 16 sin 4.æ.

A: Solution:-

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Q: Find the double integral |[ (r² + y° \do, over R={(x,y):-1<x<1,0< y< 2}. 1. R

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Hfe Rfa, bj, prove the triangle ineguatity for integrats: , ) drs (Hint: Recall that ƒ - f - S…

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Q: By rewriting the summation of the power series E (n- 1)C,x" + E, 2nC,x"-1 +E C, xn+1 = 0, we obtain:…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

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Q: (c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values…

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A: Consider the box plot that represents the data from an experiment using pendulums designed to…

Q: Evaluate: x2dz using trapezoidal method with n = 10. Round off to 6 decimal places.

A: To evaluate using the trapezoidal rule with n=10.

Q: 5. (a) Let V = R* and let (·, ·) be the standard dot product on V. (i) Calculate (e, +€3; €2 + €4).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (a) Evaluate the sum 20 30 ΣΣ2+5.2 i=0 j=0 (b) Show that nº n is divisible by 5, for all positive…

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Q: An ellipse has a length of semi-major axis of 300 m. compute the second eccentricity of the eclipse

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Q: Evaluate: e da using 1/3 and 3/8 Simpson's rule. Round off to 6 decimal places.

A: Using Simpsons 1/3 and 3/8 rule with 6 decimal places

Q: Find L{f(t)}of the following functions. Note: a, b, e, k and n are constants. f (1) = {'+1,0<1<1…

A: We evaluate the first integral using integration by parts and the second one by the formula for…

Q: х+у+2z %3D0 Solve x — у + z%3D —1 2х + у +z %3D 2 by Gaussian elimination. а. (1,-1,-1) b. (1, 1,…

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Q: Consider the differential equation (E): 2x²y" – xy' – 2y = 0. Given that y, = x2 is a solution of…

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Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

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Q: Determine if the functions in each pair are equivalent. Provide mathematical proof or justification…

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Q: Define the linear transformations T:R R2 and S: R R so that 3. X1 + X2 -X2 and S X2 -I - 12 a.) Is…

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Q: Solve the following differential cquations 1. x + x*y -sec(xy) Ans. sin x = 2x2 +C x +y Ans. y- tan…

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Q: Consider the differentia equation y" – 2xy = 0. By using power series solution about the ordinary…

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Q: Find cos 0, where 0 is the angle between two vectors a = 2i – 3j + 2k, b = -2i + 2j+6k

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Q: Without the aid of the Wronskian determine whether the given set of functions is linearly…

A: Given functions: f1x=lnx and f2x=lnx2 To show: Determine whether f1x and f2x are linearly dependent…

Q: a, A function, f(t), with period 2n is given as f(t)= +E[a, cos(nt)+b, sin(nt)]. n-l The term [az…

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Q: 3. (a) Construct a graph with six vertices and degree sequence 1, 1, 2, 2, 3, 3. (b) Construct a…

A: 3. (a) Construct a graph with six vertices and degree sequence 1, 1, 2, 2, 3, 3.   (b) Construct a…

Q: Question 3. Let (X,p) be a compact metric space. Suppose that f: X→ X is a function satisfying that…

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Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: To determine the maximum volume of the gutter.

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Q: Problem. A circle whose area is 100t m2 is cut into four segments by a vertical and horizontal chord…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x? + z?.

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Q: Which of the following is the correct form of the partial fraction decomposition of 1 x3 + 2x2 + x…

A: Here denominator is  x3 + 2x2 + x = x × (x2 + 2x + 1) = x × (x + 1)2  Thus,  x3 + 2x2 + x factored…

Q: Give the modal percentage for Class A. Calculate the missing value H if the average percentage mark…

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Q: Let V be the vector space of all functions from R to R and W, = (/:(4) = 3 +f(2)} W, =/: 2{3) =(1)}…

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Q: QUESTION 3: Mr. Daily moves to a new province and has the option to either use prepaid electricity…

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Q: 2. Let V and W be vector spaces over a field F and let L: V → W be a linear transformation. Assume…

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Q: pentagon GHJKL (not shown), 9. If the perimeter of ABCDE is 50, 25. Pentagon ABCDE AB = 6, and GH…

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Q: az and dy dz IV. Suppose z is a function of a and y, and tan Vy? + 2 6y Solve for

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Q: 8. Construct the graph of the following Matrices: Adjacency Matrix 1 2 3 4 Adjacency Matrix 1 2 3 4…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: Determine the general solution to the differential equation dy 2 e2 dr Vy n implicit form a

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Q: Solve the following system of differential equations. dw = -w + 52z dt dx 2x dt dy = 2w – 4y + 2z dt…

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Q: y = 5/(sin3x +cos3x)

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