14. Evaluate o 4y dr + 3r dy, where C is the trapezoid with vertices (0,0), (2,0), (6, 2) and (0, 2).

Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

A:

Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A:

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x = 1+2t, y=5+15t, z=-2+6t,…

A: given : the equations of two skew lines are: L1: x=1+t, y=1+6t, z=2tL2: x=1+2t, y=5+15t, z=-2+6t D…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

Q: 14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

A: Given query is to find the the distance between two skew lines.

Q: If D is the distance between the skew lines L1 x=1+1, y=1+61, z=21 L2 x=1+2t, y=5+151, z= -2+61.…

A:

Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

A:

Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

A:

Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

Q: 6. Evaluate (a + y) da dy dz, where D is the tetrahedron with vertices (0,0,0), (1,0, 0), (0, 1, 0)…

A: Introduction: The triple integral is applicable to find the volume of a solid enclosed by given…

Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

A:

Q: Show that fdx + gdy = S 36x°y?dx + 18yx*dy is independent of path: (3,6) (-2,4) (3,6) 2,4) C(3,6)…

A: The vector field is conservative if the components satisfy the test ∂P∂x=∂Q∂x. If the field is…

Q: d the values of az/ax and öz/ay at the point z - xy + yz + y' - 2 = 0, (1, 1, 1)

A: Given that  z^3-xy+yz+y^3-2=0 To find the partial derivatives at point (1,1,1)

Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

A:

Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

A:

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A: here we the formulae   the a plane have normal n→=<a,b,c> and passes through a point (x1 ,y1…

Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

A:

Q: 3.2 Evaluate (1² + y³)dz where z = r+ iy with y the path on line from z = 2+i to z = 1+ 2i.

A: Topic:- complex number

Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

A:

Q: 1. If XZ is a perpendicular bisector, what can you conclude? 2. If m<XZY 10x + 20, WZ =x+ 2; find WY…

A: Since you have asked multiplepl part question, we will solve the first 3 part of the question for…

Q: Evaluate O xy°dx + x²dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

A:

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

A:

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z 2t L2: x=1+2t, y=5+15t, z= -2+6t,…

A: Two lines in space can be skew, parallel and intersecting. Lines are skew if they are neither…

Q: 1. Evaluate ff. y dS where S is the portion of the cylinder 4x2 + 2y2 = 16 that lies between z = 0…

A: Since you have asked for a question with multiple sub-parts, we will solve the first question for…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

Q: 2. Ostain the geweval folu fion a. my = nxydx b. (@ x*+y') = {ry y' c. xy = Y(x* + sy) y' %3D

A: Given differential equation is as  my2=nxydx/dy  Note : without introduction of dy whcih cant…

Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

A:

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z= -2+6f,…

A:

Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

A:

Q: 5. Evaluate SS (x² + y²) dV,where E lies between the spheres x2 +y² + z² = 4 and x² + y² + z² = 9

A:

Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: 3. If PY = 3, YZ =5 and PV = 12, find WV. 4. If PW = YZ = 5 and PY = 10, find PV %3D %3D Z. 23

A: Topic:- secant secant method in circles

Q: Question dz If z(x, y) = x²y, x = ", and y = u'v², find

A:

Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

A:

Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: (b) xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z < 0}.

A: We have to evaluate given integral:

Q: 4 In AVYX, the centroid is Z. Use the diagram to solve the problems. A. If XR = 24, find XZ and ZR.…

A: In given triangle we have: XO=OV, XP=PY &amp; YR=RV Therefore, OY, XR &amp; PV are median of given…

Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

A: