(1 3 1 2 2 A = 2 3 1 B =1 4 2 2

Q: Calculus Find the following surface integrals. Here S is the part of the sphere x^2+y^2+z^2=a^2 that…

A: S is a surface given by parametric curve r u,v = xu,v i + yu,v j + zu,v k∫∫S   fx , y , z dS = ∫∫S…

Q: Use Laplace transforms to solve the following differential equations. a) + 5y = 3 , given that y = 1…

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Q: Given the tree below, find the following. e) Which vertex is the parent of h? f) Which vertices are…

A: 1. d is the parent of h 2.sibling of o is p 3.ancestors of m are b,g,e,f

Q: Q1. a) Find the Laplace transform of the following expression by using transform tables. f(t) = t +…

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Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to 2…

A: Given function is  fx,y,z=4x+2y+z subject to  x2+y+z2=1⇒gx,y,z=x2+y+z2-1

Q: Use either integration by substitution or integration by parts as needed to evaluate x+1 -dr x2+2r+1…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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

A: Consider the given surface, y=x2+z2 Distance of the point 0,c,0 to the surface will be,…

Q: Suppose that G and H are equivalence relations in A, and that G C H. Prove that Gr Gy if and only if…

A: Given G and H are equivalence relations in A. Let us start proving the step by step

Q: -2 Find C, where matrix C = [3/2 -1/2

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Q: The equation p =- in spherical coordinates 5 represents sphere.

A: This is a problem of spherical coordinate system, vector calculus.

Q: Test the series for convergence or divergence. Please provide detailed solution. (-1) -1 Σ 5+3n a)…

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Q: Find the matrix A. 13

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Q: 3. (1 – 3 sinh( 2t) + sinh(4t))´ dt

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Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

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Q: Given the tree below, find the following  a) Which vertex is the root? b) Which vertices are…

A: Here we use basic defnitions of tree

Q: 3. Using both Simpson 1/3 and 3/8 rules compare the Error of the equation. -dy 1+cosy

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Q: Determine the real roots of f(x) = -0.5x² + 2.5x + 4.5 Using three iterations of the bisection…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

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: Describe the graph of the equation. r = 16costi + 6 sintj – k O It is an ellipse in the x = -1…

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Q: 4 Given matrix A = : 1, find x such that -2 the matrix is singular. а. О с. 3 b. 2 d. 6

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Q: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

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Q: Solve the following system of differential equations. dx 6х + Зу — 82 dt dy 2y dt dz = x – 3z dt

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Q: faow that the function f depthed by (X .Y) = (1, - 1) f(XrY) = %3D x2 + 냉 (x, y) $ (1,-1) * ty is…

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Q: Verify the Divergence Theorem by evaluating F.N ds as a surface integral and as a triple integral.…

A: Solution:-

Q: 3. An integer n : 1<n < 1000 is chosen. Compute the probability that the integer is... a) divisible…

A: Probability of divisibility

Q: a tan Vy? + x² = z*e®%. Solve for az az and

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Q: Five mice in a stable population of 500 are intentionally infected with a contagious disease to test…

A: We will form a differential equation and then solve it to get number of mice infected after a…

Q: 5. Let o1, 02, 03 be the Pauli spin matrices (? 0 1 1 0 1 03 = 01 02 i and oo = I2. Consider the…

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Q: Consider the sequence defined by the recurrence: a0 = -1, a1 = 2, an+2 = 3an+1 - 2an (n is greater…

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Q: Instruction: Create example problem about Area Region Bounded by Different curves. Write the…

A: The area between the curves y=x2-1 and y=-x+2 on interval 0, 1

Q: Check whether the solution is balanced or not. Then, use the Northwest Corner Rule to find the…

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Q: Measure of minor arc SH= _____?

A: This is a problem related to circle. Let us find the measure of the minor arc SH in the next steps.

Q: Numerical Methods a) Employ any suitable numerical methods to estimate the water level from t = 0…

A: A table is given that shows the relation between time and velocity rate while the water is drained…

Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: 4 er substitution is performed, which of the following is equivalent to L*x³ VI +x*dx ?

A: Using substitution we solve the intregation.

Q: Suppose you have borrowed $50 from a foreign lending institution. The loan requires a payment of 6…

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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: Find the value of d. 3.

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Q: 6. tet 2 B= |-3 4 1 -4 5. 4 =) Find odj a Compute det (B) E Show that the 5 (Adj B) = (odj 8) 8 =…

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Q: The rate of cooling a metal ball can be expressed as dT 3D - k(Т — Та) dt Where T= temperature of…

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Q: 3. Considering the following two-person game, what percentage of the time should Y play strategy Y1?…

A: Solution:

Q: State whether the curl of the vector field shown below is on average positive, negative or…

A: To Explain: whether the curlF is positive, negative, or zero in all given four different regions.

Q: The one dimensional wave equation describes how waves of speed c propogate along a taught string. It…

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Q: I. Consider the function g defined by 1 g(1, y) = cos (7x/) + log3(r – y) Do as indicated. 1.…

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Q: If L {f(t); p} = F(p), then ° f(t) S dt = F(u) du, assuming that the integrals converge and hence…

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Q: 1. Assign the maximum amount to this cell that is allowable based on the supply and demand…

A: # as per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: 505. Two tangent lines at the endpoints of a given arc containing 120° are drawn, and a circle is…

A: Solution :-

Q: For f(x) = x – 2 and ao = 0, bo Apply the bisection method and calculate b2 (right endpoint after 2…

A: We have to continue the bisection method upto second iteration. Then we have to find b2.

Q: The pattern​ 1, 8,​ 27, 64,​ 125, ... is a cubic pattern named because 1=1•1•1 or 1^3 8=2•2•2 or…

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