10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

Q: Consider the region enclosed by the curves y = r² + 1 and y = 2r + 1:

A: Consider the region bounded by the curves y=x2+1 and y=2x+1 The intersection between the curve is,…

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Find the average squared distance between the origin and the points on the paraboloid z = 4 – x² –…

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Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: Suppose a sphere of radius r is sliced by two horizontal planes h units apart (as shown). Show that…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 3) Find the area of the surface obtained by rotating the given curve about the indicated line, y=x2,…

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Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

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Q: 3. Find the volume of the solid that lies between the paraboloid z = x² + y² and the sphere x2 + y²…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: 4 The area of the surface S = {(x, Y, z) E R³ : z = 5 – x² – y², z > 3} equals (A) 4ñ 9. (B) 5* 13…

A: 4 Given S=x,y,z∈R3:z=5−x2−y2,z≥3.. We have to find the surface area of S At z=3 ⇒3=5−x2−y2⇒x2+y2=2…

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 28 + 2y2 y y 21 35 30 1 25 20 5 10 15…

A: x=9y2,  x=28+2y2 The region is,

Q: 2. Find the area of the part of the surface z = cylinder x2 + y² = 9. 3xy that lies within the

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Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: find volume 26. The wedge cut from the cylinder x2 + y? = 1 by the planes z = -y and z = 0

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Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the area of the upper portion of the cylinder x2 + z2 = 1 that lies between the planes x = ±1/2…

A: Find the area of the upper portion of the cylinder x2 + z2 = 1 thatlies between the planes x = ±1/2…

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: Graph the surface 1 = y? +z? - by first sketching at least three cross sections in each of the xy…

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Q: 4. Find the area of portion of the sphere x²+y²+z = 9 between the planes z = 1 and 2 = 0. Draw the…

A: Surface area of a surface z=f(x,y)  A=∫∫D1+fx2+fy2dA Here D is a point on xy plane

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

A:

Q: 4 The area of the surface S = {(x, y, z) € R³ : z — 5 — z² - y², z ≥ 3} equals (A) 4T (B) (C) (D)…

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Q: need help with 9.2.5

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: 7. Calculate the area of the portion of the sphere x +y +z2 = 49 between z= 2 and z=V2. 2 %3D OA.…

A: Surface area of the surface given by z=f(x,y)  A=∫∫D1+fx2+fy2dA where  D is projection of surface on…

Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Consider the circle, x2+y2=25 find the equation of the tangent line,…

Q: 1. Find the surface area of the part of the sphere x+ y +z = 4 that lies above the plane z =1.

A:

Q: Find the area of the part of the sphere x2 + y2 + z2 = a2 that lies inside the cylinder x2 + y2 =…

A: answer is A = a2(π -2) detailed solution with explanation is given below

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

A:

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.