8 -2 Let y = and u = 1 -6 Compute the distance d from y to the line through u and the origin. d =

Q: QUESTION 1 Let E = {qEQ: -n<qs2} then Sup E = and Inf E: %3D %3D %3D For the toolbar, press ALT+F10…

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Q: 11. Find the value of x and the length of each secant segment. K M 3 J 2.5 5.9 x= 4; KJ = 7; LJ =…

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Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

Q: c) Sinh3u = Sinh'u + 3Cosh'u.Sinhu = 3Sinhu + 4Sinh'u d) Sinh'u- Sinh'v Cosh'u-Cosh'v

A: We have to show that the following results

Q: 12 sin°(z) dr: C is any closed curve -dz enclosing 7/6 (a) Ic 6z – T -

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Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 3.…

A: Given ∫Cz3-4x+2y dswhere C is the line segment from 2,4,-1 to 1,-1,0

Q: Use Green's Theorem to evaluate the line integral [xy dx + ( xy dx + (x² + x) dy where C is the path…

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Q: 10. Suppose that a point (X, Y) is chosen at random from the circle S defined as follows: s= (x.…

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Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: 8 (6562) 243 를-), then xo = If the length of the curve y = 3 x7 from the point (0, 0) to the point…

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Q: iv) if zy = (x)- then zx + Zy = %3D %3D

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Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

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Q: 2. t. 25 一2=6 36 find oe traces in

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Q: X = Ys e %3D (ras.t) %3D (2.1,0)

A: Here we have given u in terms of x,y,z and x,y,z in terms of r,s,t , We use above given relations to…

Q: (A) Evaluate fz dz along from z 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

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Q: (11) Suppose T is reflection across the 45° line, and S is reflection across the y axis. If v = (2,…

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Q: 10.Show that Φ(t) = Ψ(t)Ψ−1(t0), where Φ(t) and Ψ(t) are as defined in this section.

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Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: Photo attached

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Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

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Q: 2.21. Plot the following curves, locate any fixed points, and obtain asymp- totic expansions to…

A: Given : 2yk+12-5yk+1yk+2yk2=2.............(i) Taking logarithm of the given difference equation, we…

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 4.…

A: Given ∫Cy2-3z+2 dsC is the line segment from 1,0,4 to 2,-1,1

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: |-4 Let y =||-3 and u =||-4 7 Compute the distance d from y to the line through u and the origin. d…

A: Solve for the distance

Q: 2. -4 let u= dx=

A: Indefinite Integration using substitution

Q: 1. Let P, X,Q denote distinct points of E. If X is between Pand Q, show that d(P,X) d(X,Q) 1-t, for…

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

Q: - s = t? – sec t + 1 s

A: Given : s = t2-sect+1

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: 68 3 (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to (2, 3, 1) and from (2,…

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Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

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Q: If e is the angle between the two regression lines of y on x and x on y. Then 1- 7? 2. X y prove…

A: For the provided lines with defined slopes of m1 and m2, the acute angle (defined as θ) is given as:…

Q: 2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + c

A: Apply normal equation formula as below

Q: 1y(0) = 1 and y uld the particular s

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Q: (A) Evaluate z dz along from z= 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 21. |'t cosh t dt Jo

A: Note:- These are multiple question and according to our company guideline we can do maximum one…

Q: Compute sec? z + x) dr

A: Given : ∫12sec2x + xdx

Q: 25. Evaluate S.(x + Vy) ds where C is given in the accompanying figure. „(1, 1) y = x (y = x² (0, 0)

A: Area enclosed by  these two functions will be Area under the curve  Y=X minus area under the curve…

Q: Consider the path r(t) = (12t, 6t², 6 ln t) defined for t > 0.

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Q: 6. Solve Pu ay au = 0 for 0<x< 1, 0<y<1, u(x, 0) = (1 – x)², и(х, 1) %3D 0, %3D du (0, y) = 0, ax и…

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Q: Jump to level 1 Let T : U → V be a linear tran complete the information in the U R1x3 dim(U) rank(T)…

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Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

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Q: 1 hence find u Given that y =u – 5u' and x dx 2(1-15u") a. 3 u 2(15u 1) Ob. 3 u (15u? -1) 2 u'…

A: The objective of the question is evaluate the derivative and choose the correct option.

Q: if y ". y (In z) (a) Find

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Q: 7. Given paths ri(t) = (t², t°, t) and r2(t) = (In(t), e2t, In(3t)) compute the following…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1. Evaluate | (x- y)ds over the path C:r(t) = 4ti + 3tj for 0 <t<2.

A: Answer

Q: -3. Suppose z = In(6q) and q = Vv +4 tan '(5u). Find az/u and dz/dv when u dz du (u,p)=(1/5,–3) dz|…

A: Now, according to chain rule, ∂z∂u=∂z∂q·∂q∂u Given, z=ln6q and q=v+4tan-15u Determine ∂z∂q.…

Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.