3. How much work does it take to pump the water in a full tank to 2 ft above the tank in the following picture? (water weight = 64.2 lb/ft³) 2 r=3 h=6

Q: Given: 2y (y2-x) dy = dx ; x(0)=1 Find x when y=2. Use 2 decimal places.

A:

Q: Question 17 The integral represents which quantity? the total mass with density F the length of the…

A: We need to choose correct option.

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Q: Find an equation of the tangent line to the given curve at the specified point. x² - 1 y = (1, 0) "…

A:

Q: Find the general Solution of the complement of the following differential equation y" - yy) +y =oy=0

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Q: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: -4 -3 -2 -1 NWA -1

A:

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A: We have to find the area of the given region.

Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: Find an equation of the plane tangent to the following surface at the given point. yz e x² + +42=0;…

A: The given equation is;  yzexz+42=0; (0,-7,6).

Q: The position of an object at time t is given by the parametric equations x = 3t² + 1t y = 3t² + 3…

A:

Q: cos (+h)-cos(3) COS h I {+h)- - 3 3 h 3. Evaluate lim →(7/3) COS 4. Evaluate lim ₁0 π Cos

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Q: S eln (1-t) 1-t - dt ed to you in any form

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Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: (1,0), and (1,5). 5) Find the potential function of F(x, y, z) = (e² + ye*, e* + ze³,e³ + xe² ).

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Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

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Q: Use DeMoivre's theorem to compute (1+i)¹²

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Q: Find an equation of the plane tangent to the following function at (0, 0): O z = 9 O 2x +2y+z-7=0 O…

A:

Q: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

A:

Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: Calculate the area of the segment cut from the curve y = x(3-x) by the line y = x. 2 sq. units 1 and…

A:

Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: 3. A farmer applies x tons of fertilizer and y tons of pesticide to a crop, the yiled will be f(x,…

A:

Q: If the spherical coordinates (p, 0, ) of a point P are (1, 0,), then the Cartesian (rectangular)…

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Q: Find the value of the derivative of the function at the given point. 2 f(x) = 3x² − 4x; ( − 1,7) -…

A:

Q: If f (x) = x(x - 1)³, then which of the following statements is correct? f(x) has a maximum point at…

A: We have to select the correct statement from the given statements.

Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

A:

Q: 3. 2x − y = 4 at point (0,−4)

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Q: Find the Fourier transform of Hint: Use the integral formula Se-¹² du = √π e-a²₁²

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: Now find the area bounded by y= x^3, x=0, and y=3 a) 3.25 b) 3.28 c) 3.26 d) 3.27 integral…

A:

Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: If u = 0 (and neither of them are zero vectors), then the two vectors are orthogonal (perpendicular)…

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Given

Q: Evaluate the following limit, if it exists. lim (8-1/2) x→6

A:

Q: 1.) a function f f (x,y, 2) = 2-eªsing is given. of this function p= ((n 3, 31,-3) at the point what…

A:

Q: Q) choose one only 1) If y = (x − a)√/2ax − x² + a² sin-1 (*), then y' = 2√/2ax-x² - a a is…

A:

Q: In cylindrical coordinates, the equation below describes what? O a vertical plane O a horizontal…

A: Given :   r=5

Q: Find the area of are a the region i) Sketch the ii) Determine the boundarien iii.) set-up the…

A:

Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

A:

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: Evaluate csc(π/6)   Enter the exact answer.

A: Solution ) csc(π/6)  Angle in first quadrant  We know that  Sin x = 1/ csc x  x = π/6 Sin (π/6)  =…

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Suppose z = f (x, y), where x (s, t) = 2st and y (s, t) = s t + 7. af af At point P, suppose = 3 and…

A: Here we have to find a partial derivative at a point.

Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .