find a formula for the area of triangle in the xy-plane with vertices at (0,0), (a1,a2) and (b1,b2). explain your work.

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

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Q: Show that the area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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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: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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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: Find the area of the plane x+2y+2z=2 cut out by the cylinder x^2+ y^2=4

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Q: Find the approximate area of ​​the part of the plane x=z that is between the planes y = 0 and y = 6…

A: As per the question we have to calculate the area of the plane surface x = z bounded by the planes y…

Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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Q: The centroid of an obtuse triangle is outside the triangle. true or false?

A: solution ======== The centroid is the concurrent point of the three medians in a triangle. It is the…

Q: Find the area of the part of the paraboloid z=x +y² that lies under the plane 2=9.

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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, −1),…

A: Let vertex of Quadrilateral are O(0,0), P(1,-1), Q(3,1) and R(2,4)      Area of the…

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x² – y2 that lies above the plane z…

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: Find the area of the portion of the plane 3x − 3y + z = 12 that lies inside the cylinder y^2 + z^2 =…

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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: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

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: Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z…

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Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

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Q: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

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: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

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Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

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

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

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 ,…

Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.

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

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.