If tangent to a curve makes a constant angle constant angle a with fixed line, then o = ± ptan α.

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Q: A restaurant is upgrading its dining room for $20,000. The upgrade will bring in a continuous stream…

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Q: Evaluate I = f(sin x + 8y) dx + (2x + y) dy for the nonclosed path ABCD in the figure. D V C B A =…

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Q: A person wants to establish an annuity for retirement. He wants to make monthly deposits for 25…

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Q: model rocket is launched with an initial upward velocity of 65 m/s. The rocket's height / (in…

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Q: If complex numbers z₁, 22 and 23 are such that |z₁| = |22| = |23|₂ (3)- then prove that arg = arg Z2…

A: The given problem is to prove that for the given complex numbers z1,z2,z3 and |z1|=|z2|=|z3| to…

Q: Find the volume of the solid that lies within the sphere x² + y² + z² = 81, above the xy plane, and…

A: The volume of the solid is bounded by x2+y2+z2=81, above the xy-plane and outside the cone z=7x2+y2

Q: Profit ($) = -13 + 0.09 *counter Sales ($) + 0.03 * Drive through sales How many extra counter…

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Q: 5. Solve the given differential equation. x²y" - 2y = 0

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Q: Given the below function and graph, determine the following. a. A Fourier series representation of…

A: The given problem is to find the Fourier series representation of the given periodic function and…

Q: Use Green's Theorem to evaluate the line integral § 2y² dx + 3x² dy, where C is the boundary of the…

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Q: 4. Solve the initial value problem: x - 4y = x¹ ex,y(1) = 0.

A: The given differential equation is xdydx-4y=x4ex with condition y(1) = 0. The aim is to find the…

Q: 5) Let A = -4 -4 -8 4 6 4 6 4 10 Determine whether A is diagonalizable. If A is not diagonalizable,…

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Q: Let a, b, c EZ s.t. ab and at c. Prove that af (b+c), and clearly state which method of proof you…

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Q: may i please request a hand written solution

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Q: Graph the polynomial function. g(x) = -x(x-3)²(x + 2)² Choose the correct graph below. O A. G OB. Q…

A: Given polynomial is ,          g(x) = -x(x-3)2(x+2)2 which is of odd degree polynomial . Graph of a…

Q: Let G be a finite cyclic group of order n generated by x. Show that if y = xk where ged(k, n) = 1,…

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Q: 7.18. Let p be an odd prime. Determine all solutions to 2n² + n = 0 mod p.

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = 4xy + 3y², Po(-2,-4),…

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Q: 152 2 10 7 -2 -10 -1 or each of the following vect ector x so that Ax-v₂- [-5] ND L

A: We check the vectors are the elements of images or null set

Q: Find the line integrals of F = 3yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: Show that Þ(u, v) = (2u + 6, u — v, 3u + v) parametrizes the plane 2x - y - z = 12. Then: (a)…

A: Given, Φ(u,v) = (2u+6, u-v, 3u+v) The plane 2x - y - z = 12

Q: You have complex numbers Z₁ = e³-14, z2 = √√3+2i, 23 = = 3-1/2/³ 1. Write Z₁ in classical form z = x…

A: z1=e3-iπ4z2=3+2iz3=35-i32

Q: Q5. Given the system represented by the augmented matrix, solve for the value of ×₁? (Enter…

A: The given augmented matrix of the system 2-5|5 2-6|16 We have to find the value of x1.

Q: Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710 -0.125…

A: In this problem we have 3 vectors in the matrix  The standard form of vector is column vectors. Now…

Q: 4. Each of the four regions in the design below needs to be colored a different color, chosen from…

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Q: 31) Verify that Stokes' Theorem is true for the vector field F(x,y,z) = x² i + y² j + z² k, where S…

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Q: Prove the following for any given sets A, B, C and D. ACB if and only if AUB=B

A: The given problem is to prove that for the given sets A,B,C,D. A subset B if and only if A U B= B.

Q: If $5000 is invested at 5.25% compounded continuously, what is the amount in the account after 10…

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Q: The range of a linear transformation T: V→W is a subspace of W. Explain what properties must hold…

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Q: The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 + 90x - x^2/3. Find…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n' = dxn, b' = d xb and…

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Q: Diagonalize the matrix, if possible. Enter "DNE" (without quotes) in each of the answerboxes if the…

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Q: Use the Laplace transform to solve the initial value problem: 2y" + 3y' - 2y = te-²t, y(0) = 0,…

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Q: Find a set of parametric equations of the line. (Enter your answers as a comma-separated list.) The…

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Q: 1. Perform the following integrations along the indicated contours. You can use any method you like.…

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Q: If the manufacturer has 46.4 hours for painting per day, 28.4 hours for assembly per day, and 17.2…

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Q: X12

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Q: 1 L Find all points (x, y) where f(x, y) = 1 + xy. has a possible relative maximum or minimum. Use X…

A: Relative maximum and minimum by second derivative test

Q: 3. Write out the characteristic polynomials and show your work. 14y" 11y' 15y = 0, 25y" 20y + 4y =…

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Q: 1. Use formulas (2)-(5) to find the Laplace image of the given function (a) 2e-3t (d) 7sin4t - 1 (g)…

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Q: 6. Determine the points of intersection, if any, of the plane P with equation x+2y + 5z - 8 = 0 and…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j + z³k…

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Q: Country A has an exponential growth rate of 4.8%per year. The population is currently 4,612,000 and…

A: Given that Country A has an exponential growth rate of 4.8%per year.  r=4.8%=0.048 The population is…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P¯¹AP is diaconal. (If not…

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Q: Which of the following graphs have Euler circuits? K R I S H M L A: Has Euler circuit. N U T C: Has…

A: Definition: A closed trail 'T' in a graph G is called Euler's circuit if T cantains all the edges of…

Q: Compute the flux of the vector field F = : 4xi + 4yj through the surface S, which is the part of the…

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Q: 3. Consider a square C in thecz plane of R³ with vertices (0, 0, 0), (1, 0, 0), (1, 0, 1), (0, 0,…

A: Given:  Fx, y, z=x+z+ai+3aj+a2x+zk To find: ∫F.dr

Q: (1) Evaluate the following integrals. (b) C log.x (x + a)² +6² dx, where a, b > 0.

A: The given problem is to evaluate the given infinite integral of log(x)/((x+a)2+b2) for x=0 to…

Q: A right helix of radius a and slope a has 4-point contact with a given curve at the point where its…

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