Evaluate ſ. xy tan z ds where C is helix r(t) = (2 cos t, 2 sin t, t) for 0 < t < 2

Q: Calculus question in photo

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Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by 7(t) (12 sin(3t), 10 cos(3t),…

A: Let’s suppose that the three-dimensional curve C is given by the parameterization, x=x(t), y=y(t),…

Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by F(t) = (12 sin(3t), 10…

A: Given: ∫C(x+y+z)ds, where C is parametrized by r→(t)=12sin(3t), 10cos(3t), 211cos(3t) for 0≤t≤π.

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Find dy at (x, y) = (TT, T) for sin (xty) = 2x-ay %3D dx

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Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

Q: O Evalmate the impaper mitegral on e Show that it DE VERGES dx x In? (x) 2. tan (x) dx

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: dy at t = dx? Let x = 3 cos t, y = 4 sin t. Find 4

A: Derivative Question

Q: dy If x = In(sin t) and y = ln(cos t) then is %3D dx 1 cot t c) tan t 1 d) None of These а) b) cot t…

A: Given that,⇒                     x= lnsint  ........equation(1)⇒                     y= lncost…

Q: If the area enclosed by the curve x = 4 cos³ t and y = 4 sin t (wheret e R) is A then what is A?

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Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

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Q: Find the area of the region that lies inside the curve r = 2+ cos 20, but outside the curve r = 2+…

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Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: The function z = r' y is defined on the astroid r = cos 0, y = sin 0 where 0 < 0 < 2ñ. Use the dz…

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Q: dy IS let y = (cos r)m " then de sin z

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Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: dy i. Find dx of y = x* Гcos @ Isin 0 ii. Let A=| cos e l, Verify A. AT = I

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Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: 1. The limaçon x = 2 cos t – cos 2t, y = 2 sin t, 0 <t < 2m find area y

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Q: 7. Find the arc length of the following plane curve: x = e' (sint + cos t), y = e' (cost – sin t),…

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Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: O sin (z)cos(z)dz

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Q: Evaluate (2х — у) dx + (х + Зу) dy. C: arc on y = x72 from (0, 0) to (4, 32) 512/7

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Q: Q1. If f(x,y, z) = cosh?(Vx² In y) + tan-(e2y²vz) + sec³(sin vVE In x²) Find fx, fy, fz» fyx

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Q: Calculate the arc length of r(t) = (cos(t), sin(t), In(cos t)) for 0 < t < T/4. (Hint: You may find…

A: Given: rt=&lt;cost, sint,lncost &gt;

Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

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Q: 50. w = sin x + y²z + 2z, arcsin(t – 1), y = t³, z = 3 %3D

A: Since you have posted multiple question in this question which are not interlinked so I have solved…

Q: Given: z = cos(xy) dz Find: ду dz ду dz - tan(xy) = -x sin(xy) ду dz = tan(xy) = -y sin(xy) ||

A: Given: z=cos (xy)Find: ∂z∂y=?

Q: x²+y²` du du =+y dx If u=sin| ,x+y #0,Prove that x =tan u x+y dy

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Q: Differentiate implicitly to find Zx, Zy, and zxx, given: Z = xy' – sin( yz)

A: Given function is z=xy3--sinyz To find zx, zy and zxx. Solution: Implicit differentiation means…

Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: Let w = xy cos(t), y = sin(t), then d at t = T /2 is = 7/2 is dt Select one: O a. -1 Ob. 1 O c. 0

A: w=xy,  x=cost,  y=sint Now,…

Q: dv dv If V = ÷f(0) and x = r · cos 0 , y = r · sin 0 . Prove that x -+y÷= -V dr dy

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Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: Evaluate. S cos z In(sec z)dz Your Answer: In(sec z) sin - In tan z + sec + sin z + C

A: Please see the answer below.

Q: Find the intergral of  (t^2 sin(t)cos(t) +t sin^2 (t) )dt

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Q: Let z(x, y) = xy where x = r cos( 40) & y = r sin(0). dy dx ar dy dz Calculate ar dz by first…

A: NOTE: Refresh your page if you can't see any equations. . .

Q: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

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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.