A solid region Q lies within the cylinder x² + z² = 9, the plane y = 4 and the paraboloid y = 18-x²-z². a) b) c) Draw the diagram using a mathematical application Draw the projection of diagram using a mathematical application SSS z²dV using an appropriate coordinate system. Hence, evaluate

Q: at is the name of the three-dimensional shape formed if points M and N remain fixed, while line…

A: Here we have to write the name of the three-dimensional shape formed if points M and N remain fixed,…

Q: On a plane equipped with a polar coordinate system, what is the area of ​​the triangle with vertices…

A: In polar coordinate system x=rcosθy=rsinθ

Q: 2. a) Find the line of intersection of the two planes. (answer in parametric form) π₁: 4x-5y-2z=1…

A:

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

A:

Q: 6) Graph the points z = x+ iy that satisfy the given conditions:- a) z-1= 2 b) z+ 1= 1 (ans. : on…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

A:

Q: using green's theorem calculatefx'd +(4x + y ky ,where c is the vertex of the triangle (0,0),(1,2)…

A:

Q: If A(cos a, sin a), B(sin a, -cos a), C(1, 2) are the vertices of AABC, then as a varies, find the…

A:

Q: 18) B. Suppose that rectangle ABCD is dilated to A'B'C'D' using (0, 0) as the center and a magnitude…

A:

Q: 4. Describe how you can tell from the scalar equations if two planes are a) parallel and distinct or…

A: a) Given that, two planes are parallel, distinct or coincident. The general form of an equation of a…

Q: 1)² y² Consider the surface S₂ with equation 4 a) Find an equation of the trace of S₂ on the…

A: The given surface is S2 : x-124+y29-z23=1. (a) To Find and To Explain the type of conics that each…

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

A:

Q: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The plane ४/७ Incorrect y + + 6 4 SAPOR = 12 NIS = 1 intersects the x-, y-, and z-axes in points P,…

A:

Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid

A:

Q: The figure satisfies the Midpoint theorem for a triangle. Calculate (x + y) 4у x + 4 6(у-1) 4x -2

A:

Q: 1) let L be the line of intersection of the planes x+y+z=6 and x-y + 2z = 0. Find parametric…

A: To find the parametric equation for the line through the point that is perpendicular to the line of…

Q: Prove if AABC has complementary triangle AA'B'C' and centroid G, then the six triangles AGA'C,…

A:

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: Exercise 12.10. Using Properties of Dot Product Let a = (2, −3), b = (−5, 1), c = (4, −6), find each…

A:

Q: 4) What rule and unit vectors are used to do 3-dimensional graphing? Graph the plane, R = 3x-2y +62…

A: To Explain: The rules of plotting the plane R: 3x-2y+6z=4.

Q: Consider three planes P, Q and R in R3 (a) Explain in words what the intersection of P, Q and R can…

A: Let P, Q, R be the 3 planes in space. We have to study the cases of the intersection of them.

Q: Find the area of the triangle with vertices O (0,0), P (6√3, π / 6), P (12, π / 3) on a plane formed…

A:

Q: Does every second-degree equation in x, y, and z represent a quadric surface? Explain.

A: the equation of a quadric surface in space is a second degree equation in three variables. The…

Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.