(c) Evaluate . 2y² + 4z? ds, where o is the first octant portion of a cone z = Vx2 + y2 with height of 9.

Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices ±1, tj clockwise.

A:

Q: Find the area of the surface. The portion of the cone z = 4V+ y² inside the cylinder x? +y² = 16

A: Consider the provided cone z=4x2+y2 inside the cylinder x2+y2=16. Find the area of the surface. The…

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

A:

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

A:

Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

A:

Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

A:

Q: What is the ratio of the area to the perimeter of an ellipse 9x² + 25y² = 225? %3D O None of these O…

A: Topic:- geometry

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: Evaluate the following line iutegral xe-2ª dx + (x4 + 2x²y?)dy where C is the boundary of the region…

A:

Q: PICTURE

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

Q: 10. If ZYXW is an isosceles trapezoid with WY = 15x-2 and XZ = 9x + 10, find x. X 1 partn Z Y

A:

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

A:

Q: For AKMP, Q is the midpoint of KP, L is the midpoint of KM, and N is the midpoint of PM. Also, KP =…

A: we will use midpoint theorem here . when midpoint of two sides are join then the line segment is…

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: H.W : Use the Trapezoidal Rule with n=6 to approximate. Here f(x)=sin2x,23D0,b=r.

A:

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 uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

Q: Sketch the cunves x= 6-y and x t3y = 2 cnd fnd the Aea encbsed.

A:

Q: 4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going…

A: 4. The given integral is ∫C 3x2ey2dx +2x3yey2dy where C is the semicircle x2+y2=5, y≥0 To find: the…

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: Given the figure: 23)The area of R2 using vertical strip is given by A. -xkx А. С. R1 В. (x-x kdx D.…

A: As per the guidelines,we are suppose to answer only one question ( out of 27 and 28 question)…

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

A:

Q: Use the method e muiti plíers of Lagrange to fird the mini mum Value of f(^ig) = x*+4y²-22+8y…

A: Given that: fx,y=x2+4y2-2x+8yg(x,y)=x+2y=7

Q: d) The temperature at any point (x.y.z) in space is given by T= 400xyz2. find the maximum…

A:

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: O Find All the ASymploles of the Cerve 3x3 +22y-7ay²+2y"-14x4+7y²+4x+5 =0-

A: Total Asymptods are 3 .

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

A:

Q: e²+y´ dydx, where D is the circular region inside the unit circle

A:

Q: Graph and locate the foci. (z- 3) , (y+1)² = 1 %3D 25 36 Posted Wed Mar 31, 2021 at 12:17 pm…

A:

Q: Find the surface area generated by rotating the semi-circle x = (49 – y² be- tween -7 < y < 7 about…

A: To Determine :-  The surface area generated by rotating the semi-circle x = 49 - y2 between -7 ≤y ≤7…

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

A:

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

A:

Q: H.W/ A/ Find e* dr approximately using the Trapezoidal rule with n 10.

A: Given integration is ∫13ex2dx here a=1, b=3 and n=10 It means [1,3] is divided into 10 subinterval.…

Q: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

A:

Q: 1Approwimte the fellowing integmalo weiny Goucon quadrature te caith a.= 3 and Compane the nesults…

A:

Q: in R°sketch the graph of the cylinder x = (y – 2)?

A:

Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

A: Evaluate the integral ∮Csin zz2+j 2z dz, where the path C represents the boundary of the square with…

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: (c) Evaluate . 2y2 + 4z2 ds, where o is the first octant portion of a cone z = /x? + y? with height…

A:

Q: 11r If F(r) and o is the surface (x – 4)2 + y² + z² = 49 oriented 3 outwards, what is the value of…

A:

Q: Evaluate |(y zi+y°i+xzk)•d$ where S is the boundary of a cuboid defined by S -15x<1, -1<ys1 and…

A: The given integral: S=∬s(y2zi→+y3j→+xzk→) dS Where S is the boundary of cuboid defined by -1≤x≤1,…

Q: 2. Find the value of the integral 3z3 + 2 Je (z – 1)(2² + 9)dž, - 1)(2² + 9)' taken counterclockwise…

A: The solution is given as

Q: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

Q: х2, у3D 12 — х, х 3D 0, around line y — -2

A: the function given to us is y = x2 and the line about which it revolves is y = -2 we have to use the…

Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.