13. Find the intersection of [x., y.=]= [4,-2.3]+ r[1,–1,7] and| [x, y, =]=[2.-4,11]+ s[3.1,–1].

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A: Note: Multiple questions posted simultaneously, answer to the first question is given. If there is a…

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A: The given function.

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Q: 2. Compute P, and Py as a function of x, y, P.

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Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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

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Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: Is 1z = 1 for all z ∈ C?

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A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

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A: Given that plane  ,P1:x+2y-2z=5plane , p2:5x-2y-z=0line ,l:x+32=y3=z-14Normal of P1  ,…

Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: The equation of the line segment from N(3, – 4,5) to M(5,2,4), 0sts1 is a. r= (3 + 2t)i +(-…

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

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

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Q: 32. Let y = (1, 2, 6) and u = (1, 1, 1). Compute the distance from y to the line through u and the…

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Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: If u = 2-x, J x/2-xdx%3D

A: Given: Let I=∫13 x2-x dx To Find: To evaluate the given integral by taking u=2-x.

Q: #6

A: A function T; Rn → Rm is called a linear transformation if T satisfies the following two linearity…

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Q: (b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3|…

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: 21. Show that k and 7 are both zero for the line r(t) = xo + At)i + (yo + Bt)j + (zo + Ct)k.

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A: Using chain rule the given question has been solved in step 2.

Q: (1) What is the relationshi etween lines 11 and 12? wl Y = 2 y = 1+ 2t Z = 1+t

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Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.