2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

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Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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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: 8. Let, x - 1- and y -1+1 a) Complete the chart and sketch the curve represented by the parametric…

A: The given parametric equations are x=1-t2 and y=1+t. Complete the given table as follows. t x y…

Q: Investigate the direction of convexity of the curve defined by the parametric…

A: To Determine: The direction of convexity of parametric curves x(t)=a(t-sint) , y(t)=a(1-cost) ,…

Q: Consider the curve parameterized by 1 -t° + 3t2 + 3 2 X = 3 y = r - r? for 0

A: We need to find tangent.

Q: x² + y² 2 5. Select the Cartesian form of the parametric curve defined by x=6cost, y = 6 sint. 2 x²…

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Q: Find the slope and concavity of the parametric curve at the point t = (1/2), x(t) = (1/2)t² -1,…

A: To find the slope of the curve at t = 1/2, we need to find the derivative of y with respect to x:…

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: A particle is moving along the curve given by the parametric equations x=1+t, y=1−t. Determine the…

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Consider the parametric curve r(t) = (t³, -t²). Determine which of the following graphs is the…

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Q: Using the formula, Area = " y(t)x'(t)dt, find the area under the following parametric curve. x = 2…

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Q: Consider the parametric curve given by: y = t³ +9t² - 100t. At what point (x, y) does the curve…

A: The parametric equation of the curve is given as , x=et2 , y=t3+9t2-100t find the point x,y where…

Q: What is the slope at t = −2 ?

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t. Construct a table with…

A: Given problem:- Sketch the curve given by the parametric equations x= t3 - 1 and y= t2 + t.…

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: Describe and sketch the parametric curve in R given by x = cos t, y = sin t, z = sin 2t

A: The general form of the parametric equation of the curve in three-dimensional space is given by…

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: Given two points P(6, 3,1) and Q (5,0, 0), find the parametric equations for a smooth curve, C:x= 5+…

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