The VVF Ct)=<2 (os (t),2 sin (t), t> describes a helix. Find the tangent line to the helix at the point (0, 1, "/2).

Q: A stream line is a line that is everywhere tangent to the velocity filed 0 صواب ihi O

A: False

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Q: Find the length of arc of the given curve.

A: Given: R→=sin2t, cos2t,2t32, 0≤t≤1

Q: A stream line is a line that is everywhere tangent to the velocity filed ylgn O İhi O

A: Given that A stream line is a line that is everywhere tangent to the velocity field

Q: State the theorem of Arc Length.

A: State the theorem of Arc Length.   The arc length is x360°2πR. here R is the radius of the arc and x…

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Q: There are exactly two tangent lines from an exterior point to a circle. True or False? O True O…

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Q: Sketch the tangent line using the radius of circle O in the figure below.

A: topic - tangent to a circle to draw tangent to a circle, draw perpendicular at the point of contact…

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A: Given:    y = x4/8 + 1/4x2   Interval : [ 1 , 2 ]

Q: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

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Q: for the reparametri zations alt)= (t, Cosht, o), tER. Find two Curve %3D

A: Given curve is αt=t,cosht,0 We have to find the reparameterization for the given curve.…

Q: gment JK and segment HK are tangents to rcle G. J

A: Given that:

Q: The arc length of the curve y=3-4x2, where 0<x<1is [1-37/37] O 54 /37-1] 54 1-/37] O, 54 4 137/37-1]

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Q: A line tangent to a circle is always to the radius drawn to its point tangency.

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Q: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft…

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Q: find the length of the latus rectum of the curve rsin^2x=cosx

A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: The arc length of the portion of the curve y =ex with 3 <x<5 is

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Q: Construct two circles with radius Icm and 2cm respectively and centers 4cm apart, make two arcs with…

A: draw on paper 2 circles and their corresponding tangents according to the problem in the question.…

Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

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Q: Find the arc length (8) of the curve 7 (t) = ( – 2e*, – 4e*, – 2e*) fo %3D c - - -

A: Explanation and solutions is given below....

Q: Find the frenet frame for the tangent indicatrix of helix?

A: Three orthonormal vectors of Frenet frame {T,N,B} along the curve α,T=dαds,N=1κT',B=T×N where T is…

Q: . Consider point (a, b) on the graph of y = Inx and triangle ABC formed by the tangent line at (a,…

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Q: Find the arc length of the segment of the curve between the lines x-1 and x-16

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Q: A projectile is fired from the origin over horizontal ground at an initial speed of 500 m/sec and a…

A: formula used: r=v0cosαti+v0sinαt-12gt2j   it is given that, v0=500α=60°g=9.8t=10

Q: Construct the tangent lines from point P to circle O in the figure below. Type here to search

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A: The given curve is r and differentiate with respect to theta:

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A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

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Q: Find the arc length of one arch of y = sin x

A: Consider the given curve: y=sinxInterval  0≤x≤2πDifferentiate w.r.t. "x",dydx=ddxsinx=cosx

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Q: Find the arc length of the curve y = 2/3x 3/2 from (1, 2/3) to (2, 4/ 3).

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

Q: Find the equation of the tangent to the curv e y = 23 Az-12 at the point where a = 3. Answer:

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Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: 1. y = 1 - x; A(1,0), B(8,-3)

A: According to the company rule, we can answer only the first question and rest can be reposted

Q: A drive has a maximum speed of 12,000 revolutions per minute. If a disc has a diameter of 12 cm​,…

A: Given 5000 revolutions per minute

Q: O Find the length of arc of the curve y = from (0,0) to (4, ). %3D

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Q: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

Q: A circle centered at (9, 15) has only 1 y-intercept. What is it's radius ?

A: we have to find the radius of the circle

Q: Calculate Sc 2xyds, where C is the arc of x²+²=4 from the point (2,0) to the point (1,√3)

A: We know that ∫C f(x,y) ds=∫ab f( x(t), y(t) ) dxdt2+dydt2 dt

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Q: In the diagram below, XY is tangent to OCat point P. What is m2CPX? Explain.

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Q: Which is the complete formula used to find the radius of curvature?

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Q: Find all the points where r = 4 + 2sin(theta) has verticle and horizontal tangent lines.

A: Find the points on the vertical and horizontal tangent lines.

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.