Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis. IT 70 2 y = v -1 y 3 N -16 1 ])dy dy = 8π 3 2 X X

Q: Convert the complex number √3+ i into polar form. Express the angle using radians in terms of π over…

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Q: Given vectors u =(−3, 2) and v = (6, 7), find the sum u + v and write the result in component form.

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Q: armer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Given vector u= (4, -1) and v = =(2, 2), determine the value of u - 4v. Click and drag copies of the…

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Q: Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A = - -3 3 -63

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Q: Which of the following does not provide the exact value of the instantaneous rate of change at x=a?…

A: The instantaneous rate of change of a function f(x) at a point x=a is the derivative of the function…

Q: The emissions, E, of nitrogen oxides in millions of metric tons per year in the US steadily…

A: E is the emissions of nitrogen oxides in millions of metric tons per year. t be number of years…

Q: Compute the work done by a force F(x, y) = V(x²+2x+y²) on an object displeed along a curve oining…

A: Workdone=∫F.⇀dr

Q: 3. Determine the limit of each of the following functions if they exist: √x-2 x²-16 x²-x-12 x-4 a)…

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Q: 9) A particle has velocity, v(t) = t³ 101²+24t Compute the displacement - m/s. over [0, 6].

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Q: 1. Use the precise definition of a limit to show that 12 lim x-3-x-3 8

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Q: 1. Find the volume of the solid generated by revolving the region bounded by y=3x², y=0, and x=3…

A: The volume formula int_a^b pi*r^2 dx

Q: f(x) , x

A: Given data fx=1x3-x

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A: hx=x3+3x2+7 on -3,2

Q: A spherical dust particle, with a radius a=0.11mm and density of 1030kg/m3, is sedimenting in the…

A: Given a spherical dust particle, with a radius a=0.11mm and density of 1030kg/m3, is sedimenting in…

Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

A: If r(t) be the position of the particle, v(t) be the position of the particle and a(t) be the…

Q: ind a vector a with representation given by the directed line segment AB.

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Q: 1.5 a = 0.5 O -0.5 - 1.5 *b = 8 *C= 1 -202 0.5 0 -0.5 2 2 For r the above plot of the one sheeted…

A: (x/a)2+(y/b)2-(z/c)2=1

Q: SECTION EXERCISES 2.3 1. The average hourly wage paid to U.S. workers for selected years from 1970…

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Q: Given vector v = (2, 2), find 0.5v. Answer: Submit Answer

A: Given v=<2,2> We have to find the value of 0.5v

Q: What is the determinant of the matrix? [2 -3 11 24-9 3 -1 3 Α Ο B 12 C 91 D It does not have a…

A: Given matrix is÷

Q: Given vector u = (1, 2) and v = (4, -3), determine the value of 4u Click and drag copies of the…

A: The component of u perpendicular to v is referred to as s, while r is referred to as the projection…

Q: If lim f(x) = -00, then the line 24-406 Select an answer is a (an) asymptote of the graph of f(x).

A: The given information is:limx→-406+ f(x)=-∞

Q: How much will Software E cost you in the long run? $[?] Satisfied 75%. $0 $6,000 Software E Software…

A: Based on the given data we need to find the cost of the software E. This can be evaluated as…

Q: Determine for what numbers, if any, the given function is discontinuous. x-3 if x ≤ 3 9) f(x)= =√x-3…

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Q: For the following exercises, find the slope of a tangent line to a polar curve r = f (0). Let x = r…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

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Q: Calculate 3 (c COST + i sin COS the argument from 0 ≤ 0 < 2π. }] and express the answer in simplest…

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Q: Find the domain of the function. f(x)=√3x-9 The domain is. (Type your answer in interval notation.)

A: given function is f(x)=3x-9

Q: 2. xdx f- √3-2²-4

A: Solve the integral  ∫xdx3-2x2-x4

Q: Solve the equation. (4x³ + 3x¹y)dx + (x³y-1)dy=0 An implicit solution in the form F(x,y) = C is =C,…

A: We use the techniques of exact differential equations to find the general solution of given…

Q: Use the definition of continuity to determine whether f is continuous at a. 1 8) f(x)=- x2-7x a=-1…

A: Given, fx=1x2-7x To determine whether the function f(x) is continuous at x=-1

Q: Find the sum of the arithmetic series with the given information. -31, d -7, n = 5 a1 = -225 -231…

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Q: The plane through the origin and the points (2, −4, 8) and (8, 4, 4)

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Q: calculate the Taylor polynomials  T2  and T3 centered at  x=a  for the given function and value of…

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Q: Consider the given vector field. F(x, y, z) = xyz i-x²y k (a) Find the curl of the vector field.…

A: Given vector field F( x , y , z ) = xyzi - x2yk

Q: 10. Solve the inequality (3-x)(2x+1) 2-1 >0 algebraically and graph the solution set.

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Q: ㅠ Let D be an ellipse rotated counterclockwise by radians, as pictured below. Before rotation, the 6…

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Q: Determine dy dx if y=u²etanu and x = U COST

A: we shall use chain rule to determine dydx=dydududx

Q: Compute for dy dx cot(2x + ex) y = sec(2x + ex) · y = e²² csc(2x) + 2x cot (2x²)

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Q: 43. y = (4 — x²/3)³/2, [0,8] -

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Q: If lim f(a)-71, then the line 2-486 asymptote of the graph of f(x). 80 888 is a (an) Select an…

A: A line which acts like tangent but can't touch the curve upto infinite such line known as asymptotes…

Q: Write the vector as a linear combination.   RS where R=(-4,-5) S=(1,5)

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Q: Find the 102nd term of: -8, -14, -20, ....

A: Solution

Q: 6. Solve the initial value problem for x as a function of t.. dx (1²-9t+20)=1 for (t> 5), x(6)=0 dt…

A: we have given differential equation t2-9t+20dxdt=1, x(6)=0

Q: ds dt |₁=5 m/s

A: We know that the speed formula =sqrt((dx/dt)^2+(dy/dt)^2)

Q: Evaluate the integral. √² (2²₁ + EVE-6₁ +1 i+tv/t - 6j + t sin(mt)k)dt

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Q: 7. Draw a sketch of f(x) on the grid provided that satisfies all of the following criteria: • f(x)…

A: f(x) is a function -3 and 2 are zeros limx→0-fx=2 limx→-∞fx=-6 limx→-5fx exist Non continuous at…

Q: A trapezoidal plate with height hand bases a and 2a is submerged vertically in water as shown.…

A: Given that, a trapezoidal plate with height = h, Bases = a, 2a, and the weight density constant = δ.…

Q: 7 Given the complex number 2₁ = 30√2(cos+ i sin ) and 22 = 5(cos+isin), express the result of 21 in…

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