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- Consider the path of a particle given by the parametric equation x = y = -2+ cost for 0arrow_forwardFor each surface (u, v), identify the shape of the grid curves when is constant Some shapes may be used more than once. F(u, v) v v cos(u), 2, v sin(u) > Grid Curve a. parabolas b. circles c. lines d. helixesarrow_forwardAnswer the questions, and please explain the direction of motion and why.arrow_forwardFind the Cartesian equation of the image of the line x = 3 under the mapping f(z) = cos(z) and sketch the image. This image is a standard curve; name it. Indicate the direction of movement of the image point as the pre-image point moves along x = 3 from y = ∞ → y = −∞ (top to bottom).arrow_forwardFind the Cartesian equation of the curve C traced out by a point whose coordinates, in terms of a parameter θ, are (a cos θ, b sin θ). Obtain the equations of the tangents at θ = θ1 and θ = θ1 + π/2. Find the coordinates of the points of intersection of the two tangents, and deduce the Cartesian equation of its locus.arrow_forwardFind parametric equations and a parameter interval for the motion of a particle that starts at (a,0) and traces the circle x+y = a a. once clockwise. b. once counterclockwise. c. four times clockwise. d. four times counterclockwise. ..... a. Which of the following sets of equations could trace the circle x +y = a once clockwise, starting at (a,0)? O A. x= - a cos t, y =a sin t, 0sts 2n B. x=a cos t, y = -a sin t, 0sts2n C. x= a sin t, y = a cos t, 0 sts2n D. x= - a sin t, y= - a cos t, 0st<2n b. Which of the following sets of equations could trace the circle x +y = a once counterclockwise, starting at (a,0)? O A. X= - a cos t, y = - a sin t, 0sts 2n B. X= a cos t, y = a sin t, 0sts2n C. x= - a sin t, y = a cos t, 0arrow_forwardcele.. A projectile is launched at an angle of 30° to the horizontal from 6 ft above the ground at an initial speed of 150 ft/sec. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. Answer parts a through d. a. Find the velocity and position vectors for t2 0. The velocity vector is v(t) = ( . Taxthook Ack Narrow_forwardConsider the parametric equations x t-sint and y= 1-cost. Which of the following represents dx 1-sint O a. 1-Cost Ob. -sint 1-cost 1-cost sint d. sint 1-cost Clear my choicearrow_forward2.arrow_forwardFind the Cartesian equation of the image of the line x = 2 under the mapping z → sin(z). Sketch the image. If the pre-image point move on x = 3 from bottom to top, what is the orientation of the image point?arrow_forwardExercise Il. Given the curve with parametric equations, find the slope and the equation of the tangent line at the indicated point: = VE = t? y = (t2 – 4) , t>0, at the point (2,3) y = t3 – 3t , at the point (3,0) a) x = and 4 b) x = andarrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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