Which of (a)–(c) is the equation of the cylinder of radius R in spherical coordinates? Refer to Figure (a) Rp = sin (b) p sin ø = R ( c) ρ-R sin φ d. R FIGURE

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: Determine the amplitude of the sinusoidal function π -3 sin [2(z − )] + 3 Y = +1

A: Given,             y=-3sin2x-π3+1To find : Determine the amplitude of the sinusoidal function.We…

Q: V4-y? '8-x²-y² By converting to spherical coordinates, evaluate 2? dz dx dy.

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Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

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Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

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Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: Example: Find the torsion of the r= (cos t i + sin t j + tk)

A: We use the formula to find the torsion :-

Q: gure to the right as the parameter. (x, y) 12 ind parametric equations for the particle's motion.…

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Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: By eliminating the parameter t, sketch the following parametric equations x=5sint and y=6cost..

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Q: Use your parametric equations to determine the following: Maximum height Time to land Where to…

A: Disclaimer: Since you have posted the sub multiple parts for the questions ,we will solve the first…

Q: How do you solve this using polar coordinates?

A: We will find out the required result.

Q: b) A particle moves in simple harmonic motion according to the equation, s = 0 x Acos(wt)+ 0 ×…

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Q: 1. The parametric equations: x = a cos³ 0 ,y = a sin³ 0 ; 0 < 0 < 2n, define a curve called an…

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Q: The para metric Equations X= 9 -sin e and y=1-cos e for 0L0L 27 graph of the IS called a cyioid. a.)…

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Q: Express the eqution in rectangular coordinaties. (use variables x and y) r= 7cos(theta)

A: Given question:- Express the eqution in rectangular coordinaties. (use variables x and y) r=…

Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ

Q: What is the length of the polar curve r = 7 sin 0 from 0 = 0 to 0 = 2n? Enter a numerical value…

A: Length of the polar curve = ∫θ=αθ=βr2+drdθ2 dθ

Q: Sketch the graph of the following parametric (a) x = 1+t , y= 2t – 3, 2<t< 5 1 (b) x = 2t , y = 1+…

A: Here we have to draw the parametric equations:- a) x=1+t,    y=2t-3,   2≤t≤5b) x=2t,    y=11+t2c)…

Q: What is the rectangular equation of the curve fro the parametric equation below? x=3t+2,…

A: Consider the parametric equation, x=3t+2y=t+40≤t≤4

Q: Consider the Lissajous figure given by the set of parametric equations cos(5t), y = sin(3t). Select…

A: Topic = Derivative

Q: Use cylindrical coordinates. (a) Find the volume of the solid that the cylinder r = a cos θ cuts…

A: calculation of above requirement are as follows To find the volume of the solid that the cylinder r…