Question 7.Consider the solid inxyz-space, which contains all points (x,y,z) whosez-coordinate satisfies0≤z≤4−x2−y2. Which statements do hold?a) The solid is a sphere.b) The solid is a pyramid.c) Its volume is 8π.d) Its volume is16π3

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

A:

Q: Find the volume of the solid of revolution bounded by the graphs of x-1 and √x-2+1 rotated about the…

A: Given: Here are the given data, y=x-1y=x-2+1 on x-axis. To find: The volume of the solid of…

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Let G be the solid bounded by the parabolic cylinder x = y² - 2, and the planes z = 2x + 4 and z =…

A: Given : G be the solid bounded by the parabolic cylinder x=y2-2 and the planes z=2x+4 , z=4. To Find…

Q: 56. Show that the six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1)…

A: Plotting given six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1).…

Q: 2. ) If a = 3i, b = i+j, c= i – 2j then: a) Find a + b + c in in i, j form. b) Find b + 2c in i, j…

A:

Q: thus. d the point on he sphere X+y?+=4 Selution:- ans.-

A: We use Lagrange Multiplayer method.

Q: it) is the point (-1,-2,3) visible from the point (1.2, 0) if there is an opaque ball of radius 1…

A: With the help of two points  then we find x,y and z values .. Then we put x,y and z values in…

Q: 7) Find x, y, and z in the rhombus below. 12

A: Given: Length of the side of a rhombus is, a=12. One of the angle between a diagonal and a side is…

Q: Find the point on the sphere x +y +z = 4 farthest from the point (1, – 1,1). The point is ( ID:…

A:

Q: 3. Express the principal value of 1n z in rectangular form. a) z = -5 b) z = -2 + j2 c) z = √2 + j√6…

A:

Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: 4. a) Find the point on the unit sphere x² + y² + z² = 1 that is closest to (1,2,3). b) Find the…

A:

Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

A:

Q: Exercise Pustlems #: A. Deter hiine the Yp of tue difft'l eghs shorwn belou iII) yiv -y" - 4x+ 2xe.

A:

Q: 2. a) Give a representation of the cylinder y2 + z² = 16,-2 ≤ x ≤ 3 as a parametric surface. b) Find…

A:

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: Ex.: Find the area of the triangle whose vertices are A(1,-1,0), B(2,1,-1) and C(-1, 1,2).

A:

Q: Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point…

A:

Q: H.w/ Findthe forthes tand closest paints.ah the sphere x+y+2'=36 from p(l2,2).

A: I used Lagrange Multiplier to solve this.

Q: uestion 4: If two circles (x – 1)²+ - y – 3)? = r² and x² + y? – - 8x + 2y + 8 = 0 intersect in two…

A: