Prove that c(u × v) = cu × v = u × cv.

Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: Use Green's theorem to evaluate Sc(y² + x³) dx +xª dy where C is the perimeter of the square [0, 1]…

A:

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

A:

Q: Given a cubic force in one dimension: F = a(x – a) (x – b) (x – c), find the coefficient k in the…

A: Substitute x=b+∈ F=αx-ax-bx-c  =αb+∈-ab+∈-bb+∈-c  =α∈∈+b-a∈+b-c  =α∈∈2b-a+b -c∈b-ab-c…

Q: f (u, v) = (u? + v?) is not homogeneous O homogeneous 3rd degree O homogeneous 2nd degree O…

A: The solution is given as

Q: Determine la derivada direccional de f (x, y) = y In z en el punto P (1, 4) en la dirección de v = i…

A: Topic:- calculus

Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

A:

Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…

A:

Q: Show that(i × j) × j = i × (j × j)Conclude that the Associative Law does not hold for cross…

A: Using the cross products of the unit vectors i,j, k, we obtain

Q: Find ∂z/∂u when u = 0, y = 1 if z = sin xy + x sin y,x = u2 + y2, y = uy.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: If z=sin(x^2+y^2),x=vcos(u),y=vsin(u) find ∂z/∂u and ∂z/∂v.   ∂z/∂u= ∂z/∂v=

A:

Q: nto v. t of u orthogonal to v.

A:

Q: =. Let X, Y and Z have the joint pdf x² + y? + z x2 + y? + z2 (2т) 3/2 1+ xyz exp exp where -o < x <…

A: The joint density pdf of X, Y and Z is, fx,y,z=12π32e-x2+y2+z221+xyze-x2+y2+z22 Consider,…

Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

A:

Q: If f(x, y, z) = In(x7 + y +2)+V + y + z), then find fr, fy and fz at (1, 1, 1). %3D

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Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

A:

Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: Evaluate f(x, y) dS. f(x, y) = xy S: r(u, v) = 4 cos u i + 4 sin u j + vk 0 <u<, 0 < v < 1 2

A:

Q: U tt = quna %3D u(x, o) = Cos(x) Ut (X, o) = los (2x) %3D

A:

Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

Q: 4. Determine the resultant of the forces: F, = 440 N [N29°E] and F2 = 275 N [S23°E]. %3D Answer:

A: By using vector addition.

Q: The linear DE.s is called homogeneous if * R(x) is equal zero True O False O

A:

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: find the distance d(u, v) between u and v in the given exercise.

A:

Q: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .

Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

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Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if ux = v, and u,…

A:

Q: The Stokes' theorem states that: Ir = || (v-V)-n do True False o

A:

Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: The linear DE.s is called homogeneous if R(x) is equal zero True O False O

A: True

Q: In space v = (-5) ux + (-3) uy + (4) uz [m / s] speed moving q = 4 [C] load, E = (5) ux + (10) uy +…

A: The given three equations are, v=-5ux-3uy+4uzE=5ux+10uy+7uzB=8ux+9uy+4uz The values are represented…

Q: dr = 83 8= gravitational force 1. %3D dt in m/sec2 when t = 1, v= 4.

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

Q: If w = x²y - y²z³,x = rCost,y = rSint, dw z = re' , (r = 2)and(t = 0)then dt

A: Given equations - w = x2y-y2z3       ...............(1)x = rcost        ............(2)y = rsint…

Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

A:

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

A:

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

A:

Q: F(x, y, z) = xyzi+ (2ry+2) j+y°z°k conservative?

A:

Q: f(z) dz where a inside r= z-a

A:

Q: lompute dA ene of the turo erientatioh foe te gien parameluizaldeh X =0 = U t v, Z=U - V

A:

Q: find the local extrema with (binding) g = 0.

A: To determine the extrema of the function f(x, y, z) subjected to the constraints g(x,y,z)=0 Write…

Q: h(r, y) = h(0,0) = 0 3x2 + y2 (i) Prove that |h(r, y)| <ly

A:

Q: B/ show that if u(t) = d cos t + b sin t, where a and b are constant vectors |du d'u dt dt then…

A: B. Given: u(t)→ =a→ cos t+b→ sin t  where a→  and b→du⇀dt=-sin t a→ + cos t  b→d2u⇀dt2=-cos t a→ -…

Q: U R Given: ZR e ZV Prove: A RST AVUT T.

A: The solution is given in the next step.

Q: = In(x) – In(y) + *-y dr r+v Homogeneous O Not homogeneous

A: A differential equation is homogenous if ftx,ty=fx,y.

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.