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Q: Find the gradient vector field (F(x, y, z)) of ƒ(x, y, z) = x²y³ z³ . F(x, y, z) =

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Q: If w In(4xy) 22 du - cos(2yz -3), z log(t), y - 4e and z-sin(-1). Find 5 - dt

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Q: A 800-lb object is released from rest 500 ft above the ground and allowed to fall under the…

A: 1st we will formed differential equation for velocity of object , the solve it to get velocity .…

Q: * Differentiate wo.r.t x. ↑ 介 x² + 5x²y² + y² = 2 =) 2x + 2x + (5x+1). 25 dy da + 1/[(522² +1) 8²] =…

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Q: A farmer finds that if she plants 70 trees per acre, each tree will yield 20 bushels of fruit. She…

A: A farmer finds that if she plants 70 trees per acre, each tree will yield 30 bushels of fruit. She…

Q: Solve the area bounded by the parabola y2 = 4x and the line y = 2x - 4 in two ways. Answer: 2 sq.…

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Q: Use variation of parameters to solve the given system. 05 - (- 5)× + (-16) et -1 6 X(t) = X' =

A: X'=05-16X+16-16et

Q: An object of mass 5 kg is released from rest 2000 m above the ground and allowed to fall under the…

A: Given, Mass (m) = 5 kg Proportionality constant (b) = 50 N-sec/m Height (x) = 2000 Gravity (g) =…

Q: If x² +2y+3z? = x² + 2y² + 3z² = x² + 2y3 +3z3 =2, and x₂x3 +2y₂y3 +3z₂z3 = x3X₁ + 2y3V₁ +3Z3Z1 =…

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Q: ind the equations of the bisectors of the angles between e planes 2x −3+2+3-0 und 3x - 2y +62 +8-0…

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Q: Find the value of λ if 2x² + 7xy + 3y² + 8x + 14y + 2 = 0 represent a pair of straight lines.

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Q: Use graphical methods to solve this linear programming problem.

A: Given,      Maximize z=5x+4y,  Subject to,                  5x-y≤16,2x+y≥11,        x≥2,        y≤8.…

Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) 1 a +1 b f(b) (x-b) f(c)…

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Q: ²+ b² + c²p²-2(ab + bc+c

A: Part a

Q: Consider the following. B = {(-2, 12, -9), (-1, 4, -3), (-3, 12, -8)), B' = {(3, 2, 4), (1, 1, 2),…

A: As per our guideline, we are supposed to solve only first three subparts. Kindly repost other…

Q: Write general solution of 2x²y" + 5xy' + y = 0. Answer:

A: LET  x=ez⇒z=logx and D1=ddz so that xD=D1 , x2D2=D1(D1-1) SO GIVEN EQUATION REDUCES TO,…

Q: 4. Evaluate the double integral given by [" -dydz

A: Evaluation of double integral

Q: B. Find the volume of the region bounded by the sphere x² + y² +2²=9 x2 + y2 + z2=9 and the planes…

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Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

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Q: A. Find the tangent plane at x = 1/3, y = 2/3 of the surface z = ²+ln(x+y). B. Estimate z(.25, .60)…

A: x=13, y=23 Equation of surface: z=yx+lnx+y

Q: Set up the iterated double integral equivalent to ff f(x,y) dA over the given region R: i)…

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Q: Given: A = [1 3 3 202 € M3 33 (a) Find the eigenvalues of A and determine their algebraic…

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Q: A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the…

A: The amount of solution added at t minute is dv=1+cos2t. The amount of salt in 1 liter of solution at…

Q: Question 2 1. Consider a function f(x) = 4+ 6x², when x > 0. i. Provide a detailed statement about…

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Q: Given A = 03-2 00 1 compute et.

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Q: Show that 27 (5²2-4).

A: Using Congruences Theory we have to  show 27|522-4 We know a≡bmod n implies n|a-b ∴      25≡-2mod…

Q: A. Show that any sequence of positive real numbers either has a subsequence that converges, or else…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: If a₁, a2, a3, ... are in A.P., then find the value of the following determinant: ap+ap+m+ap+2m…

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Q: Amy, Jim, John, and Kelly are standing on the east bank of a river and wish to cross to the west…

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Q: { ∞ ^ > ㅣ 8. Determin S 9"+5 S

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Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

A: A series is a sequence whose nth term can be expressed in terms of 'n'.  A series is convergent if…

Q: An architect is designing a composite window by attaching a semicircular window on top of a…

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Q: Determine which theorem applies to simplify the following. It is possible that more than one will…

A: Given  Find the work done by the vector field Fx,y,z=yzcosxyi^+xzcosxyj^+sinxyk^ along the…

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: What should be the the worst percent relative error in measuring the radius of a sphere so that the…

A: Given the relative error in computing the volume is 2.39%

Q: Find the area common to the circles x² + y2 = 4 and x² + y2 = 4x. Answer: 8π/3- 2√3 sq. units

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Q: Question 2 ( a) Evaluate L{eot} b) Evaluate C{(t−2)² + sin 6t + cos 7t} c) Use the Laplace transform…

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Q: Determine whether the series is convergent or divergent by expressings as a telescoping sum. If it…

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Q: The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find…

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Q: B. For each of the following series, determine whether the series converges or diverges. (Sum from 1…

A: A Series is the collection of a sequence. Let a1,a2,...., an be a sequence then the series is…

Q: circle, and extends to the points (-2,18) and (-5,10) (these points are on the diameter of this…

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Q: Find the surface integral of the field F(x,y,z)=yi-xj+5 k across the portion of the sphere x² + y² +…

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Q: Show that the solution of the equation √√aß [1]-[*√² X Z -B #ναβ y [ ] = 0 is t where a, ß are…

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Q: System 3: System 4: dx dt dy dt dx dt dy dt = 12x - x² - xy 8y - y² - xy = 12x - x² - xy = = 12y -…

A: We are given the following systems. First: dxdt=12x-x2-xydydt=8y-y2-xy Second:…

Q: 9. A biologist has been studying the effects of environmental stressors on a population of frogs.…

A: Let at nth year the population be Pn, then % decrease in nth year is given by                 {(Pn-1…

Q: Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only…

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Q: You need to provide a clear and detailed solution for the following Questions: Question . Let W be…

A: The given subspace W of P3 spanned by S=t3+t2-2t+1, 2t2+2, t3-2t, 2t3+3t2-4t+3. We have to check the…

Q: If D is the triangle with vertices (0,0), (99,0), (99,21), then 11 D dA=

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Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

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Q: variables method if the governing equ d²y dt² d'y dx4 + c².. = 0 where c² 11

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