5. plot x?-y?=z (Elliptic paraboloid) in 3D.

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

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

A:

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

Q: WY is a midsegment of AUVX. If UV = s + 49 and WY = 4s, what is the %3D %3D value of s?

A: Midsegment of a triangle is a segment formed by joining the mid-points of any two sides. Such a…

Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

A:

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Ir te line x34+2¢, もー4t paralled he plane 3x +y+そこ子-

A:

Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

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

A:

Q: Sketch the section of the surface at y = 0. 9x^2+4z^2=36

A:

Q: the trapezoidal rule with

A: In this question, the concept of the Trapezoidal rule is applied. Trapezoidal rule One of the key…

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

A:

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Evaluate A = Se-* dx þy trapezoidal rule with n= 10. Work for 6 digit

A: Mathematically the derivative of a function is defined as f'(x)=limh→0f(x+h)-f(x)h. According to the…

Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Can two spheres a) be internally tangent? b) have no points in common?

A: a) The answer is yes. In fact, if the distance between the centers is equal to the difference of the…

Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

A:

Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

A:

Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

A:

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: 26. A cross section of the parabolic mirror in a car headlight is modeled by y = 12x. Where should…

A: Given that a cross section of the parabolic mirror in a car headlight is modeled by y2=12x. Clearly,…

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: 1. Find the points on the parabola y 8x at which the radius of 125 curvature is 16

A:

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

A:

Q: The equation of a curved road is given as y = 100+6x–0.015x² +0.0000111? Determine the places where…

A: The equation of the curved road given is: y=100+6x-0.015x2+0.00001111x3 Measure of the "Sharpness of…

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

A:

Q: Where should the point P be chosen on line segment AB so as to maximize the angle ?? (Assume a = 2…

A: Let the distance of point P from point A on line segment AB be x and let the angle opposite side a…

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

A:

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Determine the location of a point (x, y, z) that satisfies the condition xyz &gt; 0

A: In four of the eight octants xyz&gt;0 1) x&gt;0, y&lt;0, z&lt;0 (2) x&lt;0, y&gt;0, z&lt;0 (3)…

Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

A:

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: Which integral computes the circumference of the ellipse + y° = 1? %3| 2 16 — За? dx 16 — 4г2 2 -2 2…

A: As we know the differential arc length of a curve is ds=dxdθ2+dydθ2dθ  The parametric equations of…

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

A:

Q: In R', the equation x² + y + z? = 4 describes a sphere of radius 2. Select one: True O False

A:

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

A:

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.