24. A particle moves round the polar curve r = a(1+ cos e) with constant angular velocíty w. The transverse component of its velocity is A. w B. aw(1+ cos 0) C. -aw sin 0 D. aw (1– sin 0)

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given  equation r=2+3sinθwe have…

Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

Q: Find the slope of the line tangent to the polar curve at the given point. 9 11. r= 9 sin 0; 2' 6 dy…

A: The given polar curve,r=9 sin θ; -92,11π6

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

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Q: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

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Q: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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Q: 3. Find T (t) and a set of parametric equations for the tangent line to the helix given by ř(t) = 2…

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Q: Find the slope of the line tangent to the polar curve at the given point. 3 7n 2' 6 r= 3 sin 0; dy…

A: Compute the slope of the line tangent to the polar curve as follows.

Q: 7- Find the length of the curve T = e", 30 - A<0<T given in polar coordinates. a)V10 sinh(37) b)2/10…

A: Given a curve : r=e3θ   ,-π≤θ≤π We need to find the length of the curve. Let's start.

Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

A: The vector equation of the tangent line of the parametric curve r→t at point P is expressed by…

Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

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Q: dx = - sin 20 and de dy = cos 20. de Given that r= cos 0 ; The slope of the tangent line to the…

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Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 10 cos(0) + 3 sin? (0) and…

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Q: dx = - sin 20 and de dy = cos 20. do Given that r= cos 0 ; The slope of the tangent line to the…

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Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

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Q: Suppose a curve is traced by the parametric equations x = 2( sin(t) + cos(t1) %3D y = 23 – 6 cos (t)…

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Q: 6. Find the slope of the tangent line to the polar curve r = 2 cos 0 when 0 %3D You may use sin ,…

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Q: Find the slope of the line tangent to the following polar curve at the given point.   r=4−4sinθ​;…

A: Given a curve in polar form. We need to find the slope of the tangent line at a given point and also…

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

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Q: 44. A tangent at the pole to the polar curve r = 2- 4 sin 0 is af pole 0 = = D 0 = Sing 8sin

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Q: dy dx Given that r= cos 0 ; do - sin 20 and cos 20. de = - The slope of the tangent line to the…

A: Explanation of the answer is as follows

Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: dx dy = Cos 20. do Given that r= cos 0 ; = - sin 20 and d0 The slope of the tangent line to the…

A: Slopes of tangent is dy/dx . Finding dy/dx at theta = 0.

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and the…

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Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: 6. Find the length of the polar curve r = 1+ cos 0 on the interval 0 < 0 < n.

A: Given:

Q: Consider the curve. (금) 2 = 1 19 + Identify all possible parametric equations for the given curve. O…

A: In this question, we can check one by one parametric equation in the given curve.

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: 2. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

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Q: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: 4. Consider the circular helix given by 7(t) = (3 cos t, 3 sin t,4t). Give an equation for the…

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Q: 3. Let r = 1+ sin(0). Determine the rectangular point(s) (x, y) where the polar curve has a…

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Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

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Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: