Find the points on the surface z? – xy = 5 nearest to the origin. (Use symbolic notation and fractions where needed. Give your answer as a list of coordinates in the form (*,*,*), (*,*,*).) points:

Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.y = 1/(x2 +…

A: A function is symmetric with respect to the y-axis if f(x)=f(-x). Such a function is also called an…

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: 1₂x (x + y) dA, where R is the region that lies to the right of the y-axis between the circles x² +…

A: We have to evaluate the integral.

Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: The area of the region common to both circles r=16sin(0) and r=8 is:

A: Area is calculated as shown below

Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: Find the length of the secant XY in the following diagram if the radius is 6, XW= 9 and WY =XZ z а.…

A:

Q: 6) Find the area of the surface generated when the upper portion of the circle x + y? = 100 on the…

A:

Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: Evaluate the double integral 1+ 4x² + 43²&A where D is the bottom half of the circle x? + y? = 16.…

A: In polar coordinates,                                   and

Q: w.The given.surface.at. thespeeif 2.

A: Introduction:   We know that the equation of tangent plane to the surface z=f(x,y) at the point…

Q: The distance between the centers of the following two spheres: x²+10x+y²+14y+z²=-73,…

A: Given that: x2+10x+y2+14y+z2=-73      .......(1)2x2-4x+2y2+2z2+8z=-5     ........(2)

Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

A:

Q: Find the standard form for the equațion of a circle (x - h) + (y – k)² = r?. with a diameter that…

A: topic - equation of a circle

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

A:

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: Find the length of the spiral r= 402, 0ses 21.

A:

Q: 2. Find the area of the part of the surface z = cylinder x2 + y² = 9. 3xy that lies within the

A:

Q: x = t³, y = t²,0 <t < v3

A:

Q: Identify the given radius if the center lies at the origin. a. x2 + y2 = 15, 129 b. x2 + y2 = 121 с.…

A:

Q: Find the points on the surface y? = 81+ xz that are closest to the origin.

A: Distance formula is                   d2=x2+y2+z2                  d2=f=x2+81+xz+z2 Since,…

Q: Find the points on the cone z = x +y? that are closest to the point (3,-2,0)

A: Solve the following

Q: Find the value of c>0c>0 such that the area of the region enclosed by the parabolas y=x^2−c^2 and…

A:

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Find the points on the cone z2 = x² + y² nearest the point P(6,8,0).

A: Here, we need to find the points on the cone z2=x2+y2 nearest the point P(6,8,0).

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

A: to find the area

Q: The total surface area of a cone with radius x and slant height 3x is equal to the area of a circle…

A: Solution:-The total surface Area of cone=πrl+πr2    radius=x    slant height=3x⇒πr3x+πr2…

Q: Let C be the cubic region delimited by the coordinate planes and by the planes x = 2 y=2 and z=2 in…

A: the planes x = 2 y=2 and z=2 in the first octant.

Q: Find the center and radius of circle x“ + y° - 2x-4y+1=0. Prove thot (0

A: I am solving question 1. if you want other question to be solved then repost.

Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

A:

Q: ind the exact area of the surface obtained bY rotaing -- 2)2, 2sys3

A:

Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: Find the area of the region in the second quadrant that lies between the circle r = π and the spiral…

A: Second quadrant is  [pi/2 ,pi]

Q: Q: Discuss following surfaces' and the find Inte rcepts and Tra ces . ux? +4y2 + 2² - 16 =0 .

A: Given the equation is,  4x2 + 4y2 + z2 = 16 To find intercepts and traces Intercepts :  x intercept…

Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

A:

Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

A:

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c – a? is…

A:

Q: Find the points on the surface z2 - xy = 14 nearest to the origin. (Use symbolic notation and…

A: Solution is given below:

Q: Find the area of the surface generated when the given curve just sayin revolved about the x-axis.…

A: SOLUTION-

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

A:

Q: Find the points on the cone z? = x² + y² that are closest to the point (4,2,0).

A: Given :       z2 = x2 + y2  at (4 , 2 , 0)   Minimize the distance function is   f(x ,y ,z) =  (x -…

Q: Find the center and the radius r of the sphe S: a +y ++ te + 8y – 8z = -11 82 -11 %3D

A:

Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Find the points on the surface z? – xy = 2 nearest to the origin. (Use symbolic notation and…

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

Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

A:

Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

A:

Q: 10. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

A:

Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(ry)j, F = Vf(x,y), and C is the segment of the parabola y =…

A:

Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…

Q: Name the surface and draw an accurate Graph of z = xʻ in R’.

A: