You create a container by rotating the curve y = 4 ln(x-6) for y=0 to y = 9 around the y-axis. You then fill the container to a height of 2 meters with a liquid that has density 900 kg/m³. The work required to pump the liquid out of this container (over its top edge) is: Joules (Recall that acceleration due to gravity is 9.81 m/sec².)

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Q1 (a) Interchange the order and evaluate the integration a+c 2x fa* ft* xy² dydx 0 a-2 c-6

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Q: 1.5+ 1 4 In the figure, is f(x) squeezed by u(x) and 1(x) 2 1. at x = 37 ? 2. at x = 2? IT 14(X)…

A: Concept: Squeeze theorem: Suppose that g(x)≤f(x)≤h(x) for all x close to a but not equal to a.  If…

Q: Find the area of the shaded region. y = +3 (0,3) (2,7) A) 25/3 B) 352/3 C) 26/3 D) 22/3 2 x

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Q: Nx - My M If = Q, where is a function of y only, then the differential equation M + Ny' = 0 has an…

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Q: B. Find the volume of the indicated solid i) under 2x - 3y + z = 6 and above the rectangle R = {(x,…

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Q: 00 01 O-1 02 y+0 none of the choices

A: We will solve the problem.

Q: Find the Laplace or Inverse Laplace of the following as indicated 4s+12 1. s²+85+16

A: We have to find inverse Laplace

Q: How about number 2?

A: Let's solve two parallel diffrential equation problem.

Q: A ladder 6-m long leans against a vertical wall with the lower end on a level floor. The upper end…

A: Given , Length of ladder is 6m Let height of ladder on wall is x m, and base length of ladder from…

Q: The point P(2,-1) lies on the curve y = Z a. If Q is the point (x,), find the slope of the secant…

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Q: (5)  Please explain in words how a student would determine the normal vector to the direction vector…

A: explanation of determination of normal vector are as follows

Q: 2 7. A soup can of volume 700 cm³ is to be constructed. The material for the top costs 0.7cents/cm²…

A: We have to find the dimensions of the can.

Q: 5. Two lines have equations: L₁: x = 3t + 1, y = 3, z = −t + 2, teR and L₂: x = 2s +3, y = −s + 1, z…

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Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: √10-x² x = √10 sine x = √10 cote 15. What trigonometric substitution can be used to evaluate a. x =…

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Q: 7. What is the y-value in the solution to the system? A. -1 B. 5 C. 3 D. 2 8. Solve the system by…

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Q: 4- Given U=[2,2,3] and v=[1,-3, 4], and w = [6, 2, 1 following expressions) luxv| + u.W

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Q: By using double integrals, find the surface area of plane + y² -+z=c that lies inside a a the…

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when…

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Q: Question 2. The Limit of a Function For the function h whose graph is given, state the value of each…

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Q: Define the binary operation in the set of rational numbers as: a*b = ab + a-b Which of the following…

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Q: 2. A rocket is launching vertically upward from a point 2 miles east of an observer on the ground.…

A: Let's find speed of rocket.

Q: Expand f(x) = 3x as a half range Fourie.....sine.... series in the range 0.₁FX.. F... ..ans.: f(x) =…

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Q: An angle co-terminal to 19 6 11m 6 is

A: Given query is to find coterminal angle.

Q: [sin³ 4x cos 4xdx

A: We can find the answer as below.

Q: = n²-7n +3 What is the 50th term of the sequence represented by n a n for n ≥ 1?

A: Given sequence, an=n2-7n+3 , n≥1

Q: vergence of the following power series Find the radius of conver E n+ 1x² 41 n=0

A: We have to find the radius of convergence of the power series ∑n=0∞ n+1n2+1 xn.

Q: Given u = ⟨5, 1⟩ and v = ⟨11, −3⟩, what is the magnitude of the projection of u onto v? Round your…

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Q: Consider the arc L: y = 1+ cosa from (0, 2) to (,¹). of the surface formed when I is revolved about…

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Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

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Q: 1. If a= (-8,2) and b=(-1.-7) the projection a on to b=....... 2. The angle between vectors A =…

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Q: The exact value of sec 2√3 3 0-2 2√√3 3 c (55) ₁ is 6 02

A: Use trigonometric coordinate syste

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 3. Find the intersection of the following planes: ( x - 3y - 2z =- 9 == 2x - 5y + z = 3 3x + 6y + 2z…

A: We have to find the intersection of 3 planes.

Q: dx x² + 8x + 7 2

A: We know, ∫dxx-a=lnx-a

Q: Determine the absolute extrema of the given function on the specified interval. 1.) f'(x) = 1 + 80x³…

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Q: -3x₁ + x₂ + 3x3 = 0 -6x₁ + 3x₂ + 3x3 = 0 2x13x2 + 5x3 = 0 Write the solution set of the given…

A: The given system of equation,-3x1+x2+3x3=0-6x1+3x2+3x3=02x1-3x2+5x3=0

Q: on the set of rational numbers as a b = ab D. Com

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Q: can you answer question 3 please

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Q: Question 6 Find two numbers whose sum is "a", if the product of one to the square of the other is to…

A: Using algebraic operation

Q: 3 2 Given f'(x) = 2x³ + 2x² + 3x, f(x) has: a. 1 critical point b. 3 critical points c. 4 critical…

A: We have to find the critical points

Q: (x5+2x² + 1)dx x3 x³ - x

A: We know that integration of xn  is- xn+1/n+1 + C . Here C is integral cosntant.   Here i attached…

Q: Question 2 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

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Q: 12. A pie is re take the p

A: NOTE: Refresh your page if you can't see any equations. . Newton's cooing law is given by here we…

Q: Solve the following equation by using LONG DIVISION 6x³5x²49x + 60 = 0

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Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: ata Careek. The following expression represents the Riemann sum, sing over some interval [a, b], a…

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