Find proj y u where v= i+j + k, u = 12 i +3j+4 k O 20. 20 20 j+ k O 19 w/ 19 19 k i + j+ O 19 19 169 i + 169 19 k O 19 19 19 k 13 -i + i+ 13 13

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

A:

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

Q: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)

A: Solution :

Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: Q4: 16 u. nin N, then 5 bounded fo belongs t and infinum

A: We define a subsequence  an = Sin(pi/2) + (-1)n = 1 + (-1)n . So, a2n = 2 and a2n - 1 = 0.

Q: Q #2 Let X - R" and ne N and z = 3 X,.G V neN where Gn = { (miy) €R* : y>nuf. gs z a topoligy on X.…

A: Topology means it should satisfy 3 conditions  Empty set and whole set should belong to tau.…

Q: A 400 lb obJeet is neleased from rest Goo t above the ground and allowed fo fall under the influence…

A: A 400-lb object is released from rest 600 ft above the ground Air resistance  is -10V

Q: Let f(x,y) = x² – xy+y² – x. Find the direction u and the value of Duf(1, – 1) for which Duf(1, – 1)…

A: We have to find maximum directional derivative.

Q: dz dz Let z= f(x,y) , where x= u? + v? and y= Find and du at (u,v) = (- 40, - 4), given that :…

A: Please see the explanation below

Q: Which of the following represents the distance between (X. (X2. Y2) O A. d = 2 / (x2 +1) + (y2 +Y1)…

A: Given two points, A(x1,y1) B(x2,y2) distance d=?

Q: y T R 3 U Ox = 3; y = v9 Ox = 27; y = 9v10 Ox = 3; y = 3v27 O x = 27; y = 3V90 O Type here to search

A:

Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: Let f(x, y) = 9e2xy what is fxyx (x, y) =? %3D Select one: O a. 72ye2xy + 72xy²e2xy O b. 36хуе2у +…

A: Given: f(x,y)=9 e2xy ; To find the value of fxyx(x,y)=?

Q: 1. Compute u + v and u-2v where u = -5 and v = T 2

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…

A:

Q: Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy…

A: Given that f(x,y)= x^3-2xy+xy^3+3y^2 then find the fxx, fyy, fxy.

Q: uppose that w = f(x, y, z), where z = r(u, v), y = y(u, v), and z = z(u, v). 'hich of the following…

A:

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

A:

Q: In Exercises 19–22, r(t) is the position of a particle in space at time t. Find the angle between…

A: Consider the first part: Consider the following position vector: rt=3t+1i^+3tj^+t2k^ Differentiate…

Q: Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v =…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: Y XY Student Weight (kg) 72 Height (cm) 1 170 2 172 70 3 158 60 165 73 4 180 85 6 195 98 7 183 78 8.…

A: We need to calculate the correlation coefficient for the given data, student X Y XY X^2 Y^2 1…

Q: Compute F. Oszs V1-x2 –y? Let E be the hemisphere described by and F=Vz2 + x² +y² i + Vz² + x² + y²…

A: By Gauss divergence theorem:∬∂EF·nds=∭Ediv(F)dvhere givenF=x2+y2+z2( i^+j^ +k^…

Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: VW || UX. Find UY. 14 V UY Submit w/

A:

Q: f (x, y, z, u, v, w) 3æyzuvw + x²y²w? – 7cz° + 3yvw Calculate [af af af af af af + for a = y= z = u…

A: Solution

Q: Let Ebe the hemisphere described by Oszs V1-x² -y? | and F=Vz2 + x² + y? i+• v²j+Vz? + x² + Compute…

A:

Q: R(t) = −0.3t2; R'(3) R '(3) =   1B. U(t) = 5.3t2 − 1.7t; U'(3) U'(3) =

A: Differential formulas we need to used here is; Power Rule: (d/dx) (xn ) = nxn-1

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: y = (1,y) O A. 2uv %3D O B. a(u,v) -2uv (1,y) OC. d(u,v) O D. 0(1,y) 0(u,v) 24 E. None of the…

A:

Q: Which condition would prove AJKL AXYZ? K Y 7. 56 7. O A. JK XY %3D B. JL XZ 8. C. KL YZ 8. O D. JL…

A: The given sides are, KL=56  YZ=7

Q: If W=W[y,, y2, y3] where y1, y2 , y3 are twice diffferentiable, W" = W. Select one: O True O False

A: this is true because

Q: 5={cj+ kn, u +vn): nez T={(x,y)EZ:157 x +107 y =- 157 x +107y=1 choose j,K, u,v EZ, such that S=T"…

A: Linear Diophantine equation: A linear Diophantine equation in two variables takes the form of…

Q: Find r(t) given the following. r'(t) = 18t5j+20t¹k, r(0)=2i+18j O r(t)=2i+(18+ 3t6)j + 4t³k O r(t) =…

A: Given,

Q: Find y dy ·S using the substitution u +5=√√y+2 y+2 © ²(√√y+2-5) (5√/y+2+y+24) + C…

A:

Q: If u = is X then uor y OA. 33 OB. - 4 Vyx y a - 8 Vy x3 OD. 4 Vy x3

A:

Q: 5z g(x) = J. u + 4 du 7z u? +1 = (x),6 HINT: 5z u + 4 du u + 4 u + 4 du -du + u? +1 /7z u² +1 u? +1…

A:

Q: y dy Find ·S- using the substitution +5=√√y+2· Vy+2 ²(√y+2−5)(5√/y+2+y+21)+C 3…

A:

Q: Ex: Find and . fie 28. u = rs? In t; r = x², s = 4y + 1, t = xy³ %3D

A: ∂u∂x and ∂u∂y

Q: // (9x + y – 2z) dS. Evaluate S: z = x +, osxs 2, osys 3

A:

Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: Solve the P.D.E utt = 16 uxz2 s.t u(0,t)=u(5,t)=0 , u:(x,0) = 0, u(x,0)=x² (5 - x) ,h=1,k=0.4

A: See this solution in below

Q: 1. R(t) = −0.3t2; R'(3) R '(3) =   1B. U(t) = 5.3t2 − 1.7t; U'(3) U'(3) =

A: 1. R(t) = −0.3t2; R'(3) R '(3) =   1B. U(t) = 5.3t2 − 1.7t; U'(3) U'(3) =

Q: I ntegrate: Sv V v+2dv HIN T: If u =x+Q, then × = U-a

A:

Q: 4. (x - j2y) - (y- jx)=2+j (x= 3, y = 1] %3D 5. If Z=R+ jal +1/jaC, express Z in (a + jb) fortm when…

A: 4. Consider the given equation. (x-j2y)-(y-jx)=2+j The objective of the problem is to find the…

Q: If W= W[y,, y2.Y3] where y1 , y2 , y3 are twice diffferentiable, W" =W. Select one: O True O False…

A:

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

A:

Q: Find the standard matrix representing each given linear transformation.

A: Given: a) L:ℝ2→ℝ2 is defined by L (u1u2)=-u1u2            ...................(1) b) L:ℝ2→ℝ2 is…

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.