2) The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle y= - V4 - x2 to the semicircle y = 4 - x2. A) 4(4 – x2) B) 2(4 - x2) c)2V4 - x2 D) V4 - x2

Q: Find the distance between the parallel planes 2x – y + 3z = 6 and 4x - 2y + 6z = 24 %3D %3D

A:

Q: Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are…

A: Sphere equation x-42+y-52+z-22=16

Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

A:

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: Verify that the two planes −x + 6y + 2z = 3,   −(1/2)x + 3y + z = 4 are parallel and find the…

A:

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: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…

A: We can solve as follows

Q: Find the volume of a parallelepiped spanned by 2i - 5j - 7k, i-k and 9i – 3k.

A:

Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

A:

Q: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

A: Given: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

Q: Verify that the two planes −3x + 6y + 7z = 1 , 6x − 12y − 14z = 25 are parallel and find the…

A: Given equations of two planes are: -3x+6y+7z=1 and, 6x-12y-14z=25 Thus we can define the normal…

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

A:

Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

A:

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

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

A:

Q: 82. Use Theorem 6.10 to prove that a sphere of radius 5 has surface area 1007.

A: Given ,radius of sphere=5 We know, surface area (S) of a sphere of radius r units is given by:…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Sketch the surface 2./4- and verify that fry - lyx

A: Given surface is  z=4-x2-y2 we have to sketch this and verify that fxy=fyx

Q: 2. Do the three planes x + 2y + z = 4, y - z = 1, x+ 3y= 0 have at least one commom point of…

A:

Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

A:

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

A:

Q: Show that the planes given by 2x − 4y − 3z = 5 and −4x + 8y + 6z = 1 are parallel, and find the…

A: Solution:Given2x − 4y − 3z = 5 −4x + 8y + 6z = 1To prove :The planes are parellel and to find the…

Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

A:

Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of…

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved…

Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D

A: Explanation of the solution is given below....

Q: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

A: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

Q: 3. Find the orthogonal trayectories to the cuve y = ax²- acx Is held fixed. 3 .2 %3D where a

A: The curves that cut every member of a given family of curves at right angles, is called an…

Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

A:

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: 14) Determine the distance between the parallel planes: 6z = 4y - 2x; and 9z = 1- 3x + 6y.

A: Given problem:- Determine the distance between the parallel planes: 6z = 4y - 2x and 9z = 1 - 3x +…

Q: Evaluate the triple integral. JUr ryz dV where Tis the solid tetrahedron with vertices (0,0,0),…

A: Find: ∭Txyz dV Obtain the equation of the plane that contains the points 0, 0, 0, 1, 1, 0 and 1, 0,…

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: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

A:

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: Show that the maximum value of abc on a sphere of radius r centered at the origin of a Cartesian…

A:

Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

A:

Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

A:

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

A:

Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

A: