Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i+ 1j + 1k across the surface S.

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A: Sol:- At equilibrium price :- Qd = Qs 25-3P+0.2P2=-5+3P-0.01P221P2-600P+3000=0P1, 2=--600±-6002-4·…

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A: Surface area = 2πrh+2πr2 Volume =πr2h = 2π

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

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A: For the given Exact Differential (6xy3+cosy)dx+(kx2y2-xsiny)dy=0 value of k is 9 Hence option (A) is…

Q: 32. Solve the initial value problem y = (6 e*)/(3+2y), y(0) = 0 and determine where the solution…

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Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) € [0, 1]…

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Q: dy Write down a differential equation of the form dt 11 12 solutions all approach y = y' = as t→∞. =…

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Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

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Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

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

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Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: 5. Solve the following Laplace Equation With the conditions a²u a²u + дх2 дуг = 0 U (0, y) = F(y)…

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Q: CONVERSION OF UNITS Example 2: The density of gold is 19.3 g/cm³. What is the density in kg/m³?…

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A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

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Q: [11] a a Find the determinant of the following matrix: a a a b 2b X 3x 5y b 2x 3y b x 2y b X y N -Z…

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Q: Decide whether each relation defines y as a function of x. Give the domain and range. 8 X-9 y= Does…

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Q: What is the greatest common divisor of 24 and 44? n If n is a natural number such that gcd(800, n) =…

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Q: Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

A: Given,  S be the triangular region in ℝ3 with vertices at (2,0,0), (0,6,0) and (0,0,3) with upward…

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Q: Find the solution of the given initial value problem. cos t y' Y(T) = 0, t-9, y(t) = 9 y = t t> 0

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Q: Describe the graph of the equation. r = 3 cos ti - 18 sin tj + k O An ellipse in the plane z = 1,…

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Q: 11. A particle moves along a curve parameterized by r(t) = 3t² i-t² j+tk from the point (0, 0, 0) to…

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Q: 2. !. (n!)². > Show that there is no holomorphic function f (z) on any open set containing 0 such…

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Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (7y² − x² + 2) dy = 0 is exact. If…

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Q: Consider the following ODE with boundary conditions y" + λy = 0, y(0) = 0, y' KN ㅠ = = 0.

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Q: A DIGITAL CHIP MADE BY YOUR. MICROELECTRONICS DIVISION, COUNTS CONTINUOUSLY IN THE SEQUENCE: 1024…

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Q: Consider the following initial-value problem. y' - y = 2 cos(3t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: Suppose that people who own a Numberkrunch computer for home use will purchase another NumberKrunch…

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Q: To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any ε>0, choose 8>0 such that…

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Q: 5 A clerk sold three pieces of one type of ribbon to different customers. One piece was 3 yards…

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Q: Use the improved Euler's method to obtain a four decimal approximation of the indicated value…

A: Given y′=4x-9y,y(0)=2,h=0.1,y(0.5)=?Method-1 : Using formula k2=hf(x0+h,y0+k1)Second order R-K…

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A: It is given that,  D : P2 → P2  defined by  D(ax2+bx+c) = 2ax+b Then, we have to answer the…

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Sol:- A second order linear, homogeneous ODE has the form of   y''+py'+qy=0y'' -6y' +9y=0Here…

Q: Choose the letter of the correct answer. Let f: D-R and c be a cluster point of D. We say that…

A: True