Question to Sketch and state the name of the following space curves. 1. r(t) = (3+ 2t, 1- 3t, 2-t). 2. r(t) = (t2, -3t, 6), 3. r(t) = (t, 6 cos(t), 6 sin(t)). Prove that this curve lies on the surface of a cylinder.

Q: A curve Cis given by the parametric equations z = 2t –2 and y = (t- 2) where t > 0. 1. The curve has…

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Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: Question 4 please

A: Given parametrized surface S is:

Q: curve generated by the parametric equations. Indicate with an arrow the direction in which the curve…

A: Given that x=2+√t, y = t²-4t, 0≤t≤5 We have to draw graph

Q: 254. Find the distance between point A(4, 2, 5) and the line of parametric equations x=-1-t, y=-t, z…

A: The given parametric equation is x=-1-t, y=-t, z=2, t∈ℝ and the point is A4,2,5. Find the distance…

Q: 2. Sketch both parametric curves below. Then determine if they intersect. I they intersect, find the…

A: Introduction: All forms of curves that may be represented on a plane can be described by parametric…

Q: Question 3. Consider the function f(z, y, z) = 1² + y² +2z2 – 2r – 4y – 8z. The set of points where…

A: Given: f(x,y,z)=x2+y2+2z2-2x-4y-8z (a) To find the parametric equation of the curve containing the…

Q: Eliminate the parameter f in the parametric equations z(t)=√t+1, y(t) = Sketch the graph of the…

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Q: Q1. For the following parametric equations, (a) ㅠ x= = cos² t, y = 1 - sint, 0≤ t ≤ x = 1² +t,…

A: From below sketch we can say orientation of curve is clockwise direction.

Q: Create a table and ske the graph, and elimin

A: Here we have,  x=4cost, y=-3sint, 0≤t≤2π

Q: a)Find the equation of the tangent line to the curve and find a set of parametric equations for the…

A: To find the tangent equation of the line to the curve of intersection of both the given surfaces at…

Q: e parametric curve (t) = 3 sin(2 t), y(t) = . The sphere of equation The cone of equation 3. The…

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Q: O A curve is given by the parametric equations x = a cos(t); y = a sin(t) cos(t), 0<t< 2n , where a…

A: Tangent line Horizontal at points

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

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Q: 10. a) The curves F₁ (t) = (t, t², t³) and F2 (s) = (sin t, sin 2t, t) intersect at the origin. Find…

A: 10. a) The curves vec r_{1}(t) = \langlet, t ^ 2, t ^ 3\rangle and vec r_{2}(s) = \langlesin t, sin…

Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at…

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Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Consider the parametric curve given by x(t) = -2t and y(t) = t². (a) Sketch this curve on the…

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Q: a) x 3cost-3, y3sint+1,0si<2a x = 3 (ost-3 y = 3smt+| 3 (os (6)-3-0 351n(0)+/= (x,y) 8TY T/4 T/2…

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Q: It can be shown that the parametric equations x = x₁ + (x2 − x₁)t, y=Y₁+ (Y2 − y₁)t, where 0 ≤ t ≤…

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