what is equation geodesics on a circular cylinder parametrized by f(u, v)=(cos u, sin u, v) are straight lines, circles, and helices.

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: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

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: Now that we have our angular velocity, we can write our parametric equations. Remember that x = r…

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Q: Convent Cartesian equation to Parametric a) x² - y² = 4 b) y= ex et

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

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Q: The parametric equations I= 11 + (I2- 1)t, y=y+ (y2- y1)t where 0<t< 1 describe the line segment…

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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: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…

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Q: KnOwn equation x² + y² + z-9 = 0 and a point X₁(1,2,4), Determine: a. tangent vector equation; b.…

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Q: : Find the angle between the lines whose direction cosines satisfy the equations 1+m +n=0,1 + m² -n…

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Q: Find the Cartesian equation for the circle defined by the parametric equations x=1+2cost and…

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Q: With polar coordinates (3, -1), find (r, θ) for r>0 and r

A: The point in Cartesian co-ordinate is given by .

Q: Laplace equation will be а. Нурerbolic b. Elliptic c. Parabolic d. Circular

A: Since Laplace equation is  Uxx + Uyy = 0.

Q: Sketch with directio

A: Given:  Three polar coordinates. We have to sketch the graph with their directions.

Q: consider the following set of parametric equations: x = 6tanhθ ; y = 3sechθ Calculate d^2y/dx^2

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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: convert parametrici equation in rectangualr form  x=5sin t, y=4cos t

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Q: What is the polar equation of a circle of radius Va? + b centered at (a, b)?

A: General equation of a circle is given by - x-h2+y-k2 = r2              ..............(1)where,h, k =…

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: For the parametric curve x = t^2 + 2t + 1, y = 6t + 1, find the Cartesian equation(s) for all…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: The following questions are about the curve given by the parametric equations x=t+2 and y=t^2-2t a)…

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Q: c. Which of the following sets of equations could trace the circle x² + y² = a² three times…

A: The circle x2+y2=a2The parametric equation at the point (0,−a)x=−asin(t),y=−acos(t)Since there are…