(b) Find the area of the parallelogram with adjacent sides, ā =t-i+kand b = 2j- 3k (c): Find the domain and range of: 1) y 2) y 2-V

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

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

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Q: Ewaluate by the planes x=0,y=0, t:0, for

A: Given - E is bounded by the planes x = 0, y = 0, z = 0 , y + z = 1 and x + z = 1 To find - Evaluate…

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: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Find a formula for the distance from the point P(x, y, z) to the yz-plane.

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

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Q: 7. If the net was folded into a box, which sides represent the lateral surfaces? a f C e d

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k, v…

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

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Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: 3. Find the area of the portion of the surface of the plane 36x + 16y + 9z = 144 cut by the…

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Q: Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<=…

A: To Determine: Find the area of one side of the “wall” standing orthogonally on the curve…

Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

Q: Find the volume of a parallelepiped whose edges are ä = 7i+5j-k, 6-j+4k and e= 4i-3j+6k %3D

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Q: The shape of the cable in a suspension bridge is parabolic when it is suspended between two towers…

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Q: Use the Trapezoidal Rule to estimate the number of square meters of land, where x and y are measured…

A: The formula for Trapezoid rule is h2y0+yn+2y1+y2+y3+..... where h=b-an

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 4i…

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Q: Explain.

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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Q: Find the acute angle (in degrees) between the planes 5x 4y – 2z = 8 and 5x 2y – 5z = 5. %3D %3D

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Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

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 acute angle (in degrees) between the planes - 2x – 5y + 2z = 0 and 2x + 3y – 2z = 5. :-2 0…

A: The given equation in the vector form is, a=-2x-5y+2zb=2x+3y-2x Then, a=-22+-52+22=33b=22+32+-22=17…

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 surface area of the part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

Q: Find the distance between the parallel planes – 2z + y + : = 0 and 10z – 5y – 52 – 36 = 0. NOTE:…

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Q: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

A:

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 distance between the parallel planes – 2x + y + z = 0 and 10г — 5у — 52 — 36 — 0. NOTE:…

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Q: Show that D = |d1-d2l Vaz+b2+c2 P+1 represnts the distance between the parallel planes ax + by + cz…

A: Please refer the attached image for complete solution.THANK YOU.

Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the midpoint of…

A: From the graph, it is clear that B is at (-1,2) and D is at (5,-2) Now, the midpoint formula gives…

Q: The bearing of x from y is 045 and the bearing of z from y is 145 ,where x, y and z are three point…

A: Rules for solving Bearing and Distances: The reading in bearing is taken from North as per the…

Q: Find the distance between the parallel planes – 2x + y +z = 0 and 10r – 5y – 5z – 11 = 0. Note:…

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Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: How close does the semicircle y = V16 – x² come to the point (1, v5)? |

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Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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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 = √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: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Solution

Q: Find the area of the portion of the surface of the plane 36x + 16y + 9z = 144 cut by the coordinate…

A: Area of portion