In real-number multiplication, if uy1 = uy2 and u ≠ 0, we can cancel the u and conclude that y1 = y2 . Does the same rule hold for the dot product? That is, if u. v1 = u .v2 and u ≠ 0, can you conclude that v1 = v2? Give reasons for your answer

Q: If  x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 2.  (Enter your answers as a…

A: Solution: the objective is to find dy/dt

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: In real-number multiplication, if uv = uw and u # 0, we can cancel u and conclude that v = w. Does…

A: To explain: either v=w or give counter example.

Q: If MZCDB = 6y and mZACB = 2y + 10, find y. B E C %3D A

A: Consider the property of the rhombus that each of the diagonal bisects the opposite angle and the…

Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. y + 5x + 3y 5х + z + w = -7 z + =…

A: Given:

Q: use cramer's rule to solve for x, y, and z. 2x + y - 5z =-12 x  + 3y + z = 11 x + 6y + z = 23

A: see below the answer

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫12(y4 + 4y2 + 1)2(y3 + 2y) dy, u…

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Q: 16. If m/STU = (13x – 6)', mSƯ = (21x + 8)', and mUT = 143', find mST. %3D %3D U T

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: "en J(2, 9) 5y), find =(z, y) = (z, y) = -(z, y) = %3D

A: We wil find the second order partial derivative.

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

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

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: In ARST, mZR = 47°, m 2S = 3y - 7, and mT = 2(y + 10). Find the value of y. %3D %3D %3!

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Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

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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: If z = 7xy + y, find zx and zy. | Zy- Zx = %3D Zy %3D Need Help? Read It

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Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: The 300-lb block shown in the figure is kept from sliding down the inclined plane by friction and a…

A:

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y + z + = 7 5x + 3y z + 8 W…

A: Let's find.

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 3х + y + z + = -6 W 2x + 2y z + =…

A:

Q: 3] By using the properties of dot and cross product, prove the following: a) (w x v). ū = 0. b) (w –…

A: the cross product of a and b = ab sin(theta) the dot product of a and b = ab cos(theta) also, a…

Q: Calculate the cross product between a(3;-3; 1) and b(4; 9; 2). BIU SI E : E

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Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

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Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

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

Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: dz du (u,v)=(1,1) -2.6 Let z= 1y- 4x, =u'u and y=v - 3u . Compute a)-324 b) -328 C)248 d)312 e)316

A: Use concept of partial derivatve

Q: 3] By using the properties of dot and cross product, prove the following: a) (w x ū). ū = 0.

A: To prove- w→×v→.v→=0 The cross product of two vectors…

Q: Prove that the area of a square whose diagonal has length d is A = A = 1/2d². A square with a…

A: A square has diagonal length of d, we have to find its area.

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and…

Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: If a = i + j + 5k and b = i + j + 3k, compute the cross product aXb

A: We have to find cross product

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

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Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: State De Moivre's theorem and if z 7+ j4, find z5 using the ( theorem.

A: Given query is to find the value of z5 using De Moivre's theorem.

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.