Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y =x2 4 In(x),…

A: Given curve is y=14x2-12ln(x) Differentiate with respect to x. dydx=x2-12x

Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

A:

Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   y = 1 -x2…

A:

Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

A:

Q: Sſcos( dxdy y-x y+x D

A: Given and u=y-x,  v=y+x where D is the trapezoid with vertices (1, 0), (2, 0), (0, 2) and (0, 1).

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

A:

Q: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

A:

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

A:

Q: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

A:

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A:

Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0).…

A: Given problem:- Find the coordinates of the point(s) on the curve y = √(x + 3) that are closest to…

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: Find the total length of the cardioid r= a(1+cos 6) O a. 4a O b. 8a O c. 2a O d. a O e. 16a

A: The total length of the cardioid can be found by using the formula 2∫r2 + (drdθ)2dθ

Q: Find the point on the curve y = Vx closest to the point (1,0).

A:

Q: + y² – z dS where S is the part of the cone z? = r? +

A:

Q: Let S CR³ be the portion of the graph of the cone z2 = x² + y? which satisfies 0 s z < 1. Using…

A:

Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: (c) Evaluate . 2y² + 4z? ds, where o is the first octant portion of a cone z = Vx2 + y2 with height…

A:

Q: Consider the cone shown below. If the height of the cone is 3 and the base radius is 2, write a…

A: Given height of the cone is 3 units Radius of base is 2 units. We have to find parametrization…

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 points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

A:

Q: A coast artillery gun can fire at any angle of elevation between 0° and 90° in a fixed vertical…

A: A coast artillery gun can fire at any angle of elevation between 0° and 90.

Q: The figure below shows contours of g(x, y) on the region R, with 9 < x < 15 and 6 < y < 12. 12 -2 10

A: given region 9≤x≤15 and 6≤y≤12 using △x=△y=2 find an overestimate and an underestimate for ∫Rgx,ydA…

Q: Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 %3D and…

A:

Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: Find the coordinates of the point(s) on the curve 2y = 10 – a² that are closest to the origin. а) О…

A: Given that

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Given the equation of the cone, what is formed when: a. z = k, k + 0 b. y = k, k +0 C. X = k, k + 0…

A:

Q: = x² + y² that are Find the points on the cone z? closest to the point (1,-1,0)

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: To find the points on the cone z2 = x² + y? that are closest to the point (6, 3,0) , we need to…

A: Proceed as shown below

Q: ...) The figure below shows contours of g(x, y) on the region R, with 9 < x < 15 and 2 < y < 8. 7 6…

A: Consider the provided question, R=x,y| 9⩽x⩽15 and 2⩽y⩽8Using ∆x=∆y=2, break the region R into 9…

Q: Evaluate f, (2x? + 2y2) dS, where S is the portion of the cone z2 = 8x2 + 8y2 for 0szs 4V2.

A:

Q: Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y? = 36. Find the…

A: follow next step

Q: in R°sketch the graph of the cylinder 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 c > 0 such that the area of the region enclosed by the parabolas y = 390. c and y = c² – a? is…

A: we know that areaA of the region enclosed by given parabola is given by A=2∫-ccc2-x2dx=4∫0cc2-x2dx…

Q: Find the points on the cone z? = z? + y² that are closest to the point (-2, 5, 0). Please show your…

A:

Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

A:

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: (c) Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 and…

A: