or hwk (2).PNG X Edit & Create v + Add to 14. K'(-8, 6) is the image of K after a translation along the rule (x, y) → (x – 3, y + 6). What are the coordinates of K?

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Q4/ Find the abs.max cand abs, min Valuse of the Runctia Kcx, y) = I+xy-3x on the closed regen…

A: We have f(x, y) = 1+xy-3x ∂f∂x = y-3, ∂f∂x = 0, y-3 = 0, y = 3 ∂f∂y = x, ∂f∂y = 0, x=0 So one…

Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

A: Find the image of (5,-1) and preimage of (-6,7)

Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: Given that the equations xyuv =1 and x + y+u +v = 0 can be solved for y and v as functions of x and…

A:

Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

A:

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) ► (x - 15, y)…

A: We first find the coordinates of U,V and W U=(3,6), V=(6,3), W=(12,6) Then we apply (x,y)→(x-15,y)…

Q: 2. Find the images of the mapping W= z2 of the line y = 2.

A:

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: L' M' Which describes how the transformation affects the coordinates of the vertices of trapezoid…

A:

Q: The transfomation takes points from the xy plane to v= 3x Jx=? that takes points from the uv plar V=…

A:

Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

A:

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

A:

Q: Part (a) Evaluate 4e*dz, where C is the polygonal path consisting of the line segments from z = 0 to…

A:

Q: 11 Find the coordinates of the image of J (8,7) after a reflection over the x-axis. AY 10 8 4 2 -10…

A: find the coordinates of the image of J8,7 after a reflection over the x-axis solution let a,b be the…

Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

A:

Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: 4. that has the asymptotes x 7 and y = 6. Write an equation for the translation of y = 4 Oy=ー+7 -6 4…

A:

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) (x- 15, y)…

A: Given: The △UVW has done two transformations 1) x,y→x-15,y 2) Reflection across x-axis

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

A:

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

A:

Q: 2. Let C be the closed path constructed by joining the segment [-2, 2] on the real axis with y(t) =…

A:

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

A:

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

A:

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

A:

Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

A:

Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A:

Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

A:

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

A:

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…