Find the minimum value of the function f (x, y) = 16x² +81y² subject to the constraint xy = 1.

Q: For a quadratic equation: ax2 + bx + C = 0 where a#0, %3D state the equation of the axis of…

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Q: Q-5: a) Find the area of the region enclosed by the two graphs y = e²x and y = 1-x, on [0,1]. b) L…

A: Sol:- aThe area between curves definitionThe area between curves is the area between a curve fx and…

Q: O Represent the parabola 4=2文+1 by a vector valued funchion and sketch it (show everything !)

A: A parabola is a conic section. When a plane parallel to another plane and tangential to a right…

Q: Consider the following vectors 3 ------ -2 y = 0 |ly|| = What are the norms of the three vectors? =…

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Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

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Q: Cosine of Angle of Rotation (3d) The following matrix is the matrix of rotation. Find the cosine of…

A: Consider the given rotation matrix, Q=-23-13-2323-23-13-13-2323 Here we need to determine cosine of…

Q: 14. Consider unit-s +-sped helix B (s) = C3 cosC ), 3sin( 등 ), 뜸 The frénet - Sewret apparats of B…

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Q: O Use polar coordinates to evaluate the integral V2² + y²dxdy. -V9-y2 got sdi wolod bas sitt od

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Q: Axis of Rotation (3d) The following matrix is the matrix of rotation. Find the axis of rotation.…

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Q: 9. y'+ 2x y = x e*2 subject to IC: y(0) = - 1 10. (x + 1) y' + y = In x subject to IC: y(1) = 0

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Q: a) Explain what it means, by definition, that a polynomial m(x) € P(R) is the minimal poly- nomial…

A: Definition Let  be a A*A matrix. An annihilating polynomial  (i.e., such that m(x)=0) is called a…

Q: An equation of the form t²y" + aty' + By = 0, t > 0, where a and 3 are real constants, is called an…

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Q: 7. Find the directional derivative of the function f(x, y, z)=(y+28) at (2, 1, 1) in the direction…

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Q: Show that the formula gives the decomposition odd function. e* = cosh(x) + sinh(x) of the function…

A: Even function: Let fx is the real-valued function, where x is the real number, then, fx is an even…

Q: P2 Consider the two power series (3x)2n+1 f(x) = x + Σ (2n + 1)! n=0 (x + 1)" g(x) = 3n ln(n) n=2…

A: We will show that f(x) satisfies the given equation (y=f(x))

Q: Question 1 Suppose you make deposits into an investment account. These deposits occur in a sequence…

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Q: PS2.1 Determine if b is a linear combination of a₁, a2, a3. If so, express b as a linear combination…

A: Here,

Q: Consider the primal linear programming problem below. Maximise x1 + x2 +5/4 x3, subject to 8x1 + 3x2…

A: For the solution follow the next steps.

Q: se Green's theorem to find the work done by the force F(x, y) = x(x + y) i + xy²j in moving a…

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Q: Find the average value of f(x) = ²√√92+z³ on the interval [0,2]. farg Report all answers accurate to…

A: Sol:- Average function value definitionThe average value of a function fx on an interval a, b is…

Q: Find the radius of convergence and interval of convergence of the power series n=1

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Q: A) Find the contour integral z²dz when C is a parabolic part y = O(0;0) to point P(1;2) P(1, 2)…

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Q: 4. Log-linear models are often used to model contingency tables. In (a) terms of table and model…

A: Given information:   2000 2005 2010 2015 7.5 to 7.75 42 37 39 26 7.75 to 8 37 45 40 39 8 to…

Q: 11) A baseball team is trying to determine what price to charge for tickets. At a price of $10 per…

A: Find maximum revenue using derivatives

Q: Vrite the equation in spherical coordir (a) 5z2 = 8x2 + 8y? %3D

A: In this question, the cartesian coordinate system is transformed into the spherical coordinate…

Q: 2. The differential equation for free motion of a spring-mass-damper system is: d?x dx + 2y +kx= 0…

A: Given: Let us consider the given differential equation, d2xdt2+2γdxdt+k2x=0 where…

Q: Find the solution and define The interval at which function is değine 2. dx

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Q: y = 14. If u +4 u-4 and U= √x + x 10 dy , find dx when x=4.

A: This question can be solved using the concept of derivatives.