Find the surface area of the portion of the semi cone z = x2 + y? that lies between the planes z = 6 and z = 14.

Q: Find the surface area of the part of the plane z = 5+ 7x + 2y that lies inside the cylinder a2 + y?…

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Q: 3. Find the volume of the object cut from the cone z = Vx² + y² by the plane z = 1.

A: The volume of a solid can be obtained by considering a small volume element and integrating within…

Q: Find the volume of the solid bounded by the ellipic paraboloid z = 1 + 2x? + 3y°, the planes x = 2…

A: Given query is to find the volume of the solid.

Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: Find the volume of material cut from the solid sphere r2 + z2 <=9 by the cylinder r = 3 sin u.

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Q: b) Find the volume of the solid enclosed between the cone z = hr² and the plane z = 2h.

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Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x? + y2 =…

A: Consider the formula for the Surface and the function f(x,y).Calculate fx and fy by partially…

Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8 that lies inside the cylinder x?…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder a2 + y?…

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Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+y =1.

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Q: Find the area of the part of the cylinder y2 + z2 = 4 in the first octant, cut out by the planes x =…

A: Given. We are given a cylinder in the first octant.. y²+z² = 4 We need to find the volume of the…

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder 22 + y?…

A: We have to find surface area of the plane z=5+4x+3y that lies inside the cylinder x^2+y^2=16.

Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Find the surface area of the portion of the cone z? = 4x? + 4y? that is above the region in the…

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Q: Use​ Pappus's theorem for surface area and the fact that the surface area of a sphere of radius a is…

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Q: * Find the surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Find the center of gravity of the homogeneous plate placed in this region by showing the region…

A: Given that  The equation of two circles x2+y2=4xx2+y2=13x and the lines on the coordinate axis…

Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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Q: Find the volume of the solid that lies within the sphere x² + y + z² = 81, above the xy plane, and…

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Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

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Q: Find the volume of the solid that lies within the sphere x2 + y2 + z² = 36, above the xy-plane, and…

A: The sphere is x2+y2+z2=36 and cone is z=x23+y23. Substitute x=ρsinϕcosθ,y=ρsinϕsinθ,z=ρcosϕ in…

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

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Q: Find the surface area of the part of the plane z = 2 + 6x + 3y that lies inside the cylinder a? + y?…

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Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: nd the surface area of the portion of the cone z = Vr² + y² in between the planes z = 3 and z = 4.

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Q: Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 9, above the xy-plane, and…

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Q: Find the surface area of that part of the plane 3x + 10y + z = 9 that lies y? inside the elliptic…

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Q: Find the volume of the solid enclosed by the cone z = √(x2 + y2) between the planes z = 1 and z = 2.

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Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Find the area of the surface.The part of the surface  z = xy that lies within the cylinder x2 + y2 =…

A: Consider the formula for the surface area.Find Zx and Zy by partial differentiation .

Q: Find the volume of the solid that lies within the sphere x2 + y² + z² = 64, above the xy-plane, and…

A: To find the volume if the solid within the given sphere above xy-plane and below the cone:…

Q: Find the volume of the solid that lies within the sphere x² + y² +2²=81, above the xy plane, and…

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 5 + 4a² + 3y?, the planes a and…

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Q: Find the volume of the solid enclosed by the cone z = sqrt(x2 + y2) between the planes z = 1 and z =…

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Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.