



5. (20 points) Given a line segment L1, defined by the parametric equation to follow, find...
7. [-12 Points] DETAILS ROGACALCET3 11.1.033. Find parametric equations for the segment joining the given points. (3, 1) and (5, 4) c(t) |),osts 8. [-12 Points] DETAILS ROGACALCET3 11.1.049. Use the formula for the slope of the tangent line to find out for the curve c(t) - (543, 48 - 5) at t = 3. dy dx - 3 9. [-12 Points] DETAILS ROGACALCET3 11.1.062. Find an equation of the tangent line to the curve c(t) - (962 - 6,612...
need help
Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
the straight line L1 is described by the equation 3x + 4Y + 5 = 0. the straight line L2 is perpendicular to L4. lines L1 and L2 intersect at the point (1, -2) Give an example of another point than (1, -2) located on L2
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
2. Find a vector equation and parametric equations for the line segment that joins P to Q: P(-2, 4,0), Q(6,-1,2)
3. Find a parametric equation of the line that contains the points (1, 1) and (-2, 4). What values of the parameter should be used to describe the half-line starting at (1, 1) and going through (-2, 4)? What values of the parameter should be used to describe the line segment between (1, 1) and (-2,4), including both endpoints?
4. (10 points) (a) Find a parametric equation and symmetric equation of the line that pases through the point (2, -1, 3) and is parallel to the vector 7 +27 -37. (b) At what points does this line intersect the yz-plane?
Q4 (8 points) (a) Find parametric equations of the line passing through the point A(5,-2,9) and perpendicular to the plane 3.x - y-6z+ 2 = 0. (b) Find two planes that intersect along the line.
Find parametric equations for the segment joining the given points. (1, 3) and (3,6) c(t) = { 1 +31, 2+36 ), ostsi
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.