If the sum of the sides of a triangle is the constant 2.s, then the area is greatest when the triangle is (a) isosceles (c) equilateral (b) right angled triangle (d) None of these

Q: I. Show that the function f defined by 1, (x, y) = (1, – 1) f(x, y): x2 + y (x, y) # (1, – 1) x +y…

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Q: The Wronskian of the vector functions X= e2 and X3= Select the correct answer. 45e -55e 45e -45e-6 O…

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Q: Consider the function f(x) = x2+1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: Q3: Construct a 3rd order Lagrange polynomial of the function f(x) = Inx.cosx where x e [1, 4]. Then…

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Q: Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3X 3 = 2 -2x1 + x2 – X3 = 1 х1 —…

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Q: Let / be the line described by the Cartesian equations • X=1 y-11= 2(z-8) Let , be the line…

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Q: In n 6. En=1 0o(-3)" 2 00 n%3D1 71 (comparison test) 7. En=0 8. ΣΤ- n2+n+2

A: The main objective is to determine the series is convergent or divergent.

Q: The expression x²+2x²y=2xy+2xy°-3y² is equal to x+y

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Q: 1 2 Q1) find eigenvalue eigenvector of A=(0 1 1/ 1 1

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Q: Find the equation of the tangent and the equation of the normal to the curve y = x + at the point…

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Q: Let S = For which vector v the set S forms a basis For R?? Select one: none of the others

A: According to our guideline, we can solve only first one of multiple questions. So, here we solve…

Q: 11. Consider the weighted voting system [g: 8, 4, 2, 1]. Enter your answers as percentages to two…

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Q: For f(x) = x Apply the bisection method and calculate bz (right endpoint after 2 iterations) - 2 and…

A: The equation in form f(x)=0 is called a transcendental equation. The bisection method is a…

Q: 3. How many meters/second (m/s) correspond to a speed of 57 miles per hour, given that 1 mile equals…

A: Given that 1 mile= 5280 feet. 1 foot = 12 inch. 1 inch = 2.54 cm.

Q: Q2/B) Solve the following differential equation by using homogenous D.E method dy %3D dx

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Q: 1) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 2.1., # 40) Using polar…

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Q: Find the equation of the tangent and the equation of the normal to the curve y = x + + at the point…

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Q: onsider the function f(x) = = x* + 2x. a) Find the x- and y-intercepts of the ronh of € Gf onu)

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

Q: Question 2 [ a) {:- ): Explain why the following series (-1)" 1+ n3/2 n=1 is Alternating. b) i…

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Q: 2) Find the volume of the solid under the plane z 3x + y and above the region determined by y = x'…

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Q: C. Find the moment of inertia about x-axis of a thin plate bounded by parabola (x = y- y) and line…

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Q: B- Solve the differential equation y"-y = e* +e

A: First we will find the solution to the associated homogeneous differential equation (complementary…

Q: (-1) "-'b,. 12" +2 where b (n+ 2) 14"+3

A: In this question, the concept of convergence is applied. Convergence The feature of approaching a…

Q: Solve the differential equation y"ty=tan'x

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Q: dz dz and ду Suppose z is a function of a and y, and tan Vy² + x² = 2e6y. Solve for

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Q: 3. Show that the differential equation (cos z + 2y) dy + (r³ – y sin z) dr = 0 is an exact equation…

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Q: The formula for ordinary Simple Interest:        t=?

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Q: In Exercises 21 and 22, the coefficient matrix of the system of linear equations is not strictly…

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Q: 4) m<D in triangle DEF (not shown) is 45 degrees. Lily solved for <E using Law of Sines. She got 67…

A: Given: In triangle DEF, m∠D=45° and m∠E=67. To determine: Is the given case is ambiguous.

Q: Show that

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

Q: If a line is parallel to the vector 8i + 5j+3k and passes through the point P = (6,2, 4), then the…

A: The line which is parallel to the vector  ai + bj + ck and passes through (x1 , y1 , z1) has the…

Q: ) Use six rectangles to find estimates of each type for the area under the given graph of f, the…

A: To use six rectangels to find estiamates of each type for the area under the given graph.

Q: These numbers go in here: These numbers come out: 22 28 34 40 (? Can you work out what happens in…

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Q: Compute the following integrals (i) I = f 8(9- 10x? + x*) cos(Tx) da. (ii) I = S 6(x(1 – a?)) x (1–…

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Q: 13 If Set A = {1, 2, 3, 4}, Set B = {3, 4, 5} and Set C = {4, 5, 6} then, prove  (AUB)UC=AU(BUC)

A: The union of two sets A and B is equal to the set of elements that are present in set A, in set B,…

Q: W, = (S:{(4) = 3 + f(2)} W, =S: 2(3) = (1)} W, = (S:(5) = 0}. Then (a) W, alone is a subspace %3D…

A: We answer all these questions using the properties of vector subspaces. The detailed answers is…

Q: Which one of the following series is divergent by comparison test? n=1 n°+ 8 8. n6 Σ 10 n=1 n+9 Σ n-…

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Q: Q3) Define series symbolically: 1 1 1 1 2 3 4 1 - 4 (n+2) 1x2 2x3 3x4 nx(n+1) 1 1 -1 - 3 9 3n п 2п…

A: Solution

Q: 3. You wish to fence in a rectangular garden in your back yard, with one side of the garden against…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Express cos (a) in terms of cos(2a). Express sin? (a) in terms of cos(2a). cos²(a) Choose... sin (a)…

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Q: . Consider the function g defined by 1 g(x, y) = cos (Tx y) + log3 (x - y) Do as indicated. 1.…

A: As per policy, we are allowed to answer only 1 questions at a time. So, I am answering the first…

Q: Let Zn be the integers mod n under modular addition a) Suppose that n >1 is odd. Show that 2 is a…

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Q: II. Consider the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y)" Do as indicated. 2.…

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Q: If a line is parallel to the vector 3i + 2j + 1k and passes through the point P = (1,3, 8), then the…

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Q: 2) . Consider the function: 0 <t < 5 0, f(t) = e-kt 5 <t. A) Use the definition to find F(s) =…

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Q: It is possible to find a value for a so that the series 00 1+ n° Σ na+1 n=1 is convergent. Şelect…

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Q: Solve for x and y the followinglsystem of simultaneous equations 2 In(x) = In(y) + In(4) e*e = e?…

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Q: A small box measures 10 in by 7 in. by 3/4 in. High . Find the volume of the box.

A: Note: The volume of a rectangular box / cuboid is found by multiplying the length by the breadth by…

Q: A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution…

A: To solve the nonhomogeneous differential equation use the undetermined coefficients. Negative…

Q: x³-5 Find the domain and the vertical asymptotes, if any, of the following function x²+11x+10° a.…

A: We have to find the correct option.