Ae ete (a) Determine the rectangular equation that is parameterized by these equations et -et 2 3...
help me with this problem 1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x= 9coso , y = 5sino 2. Determine all horizontal, vertical, tangent lines if any: x= tsint + cost, y = sint – tcost 3. Find the area of the region common of Interior of r = 2 – V3sing and r= –2 + V3sino 4. Find the arc length enclosed by r = 2(1 + cose), and r = 2 5. Find the slope...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding derivative functions are x) 2/(1+0) YO (2+1) where to is in units of seconds and the units on the coordinate axes are feet (a) The horizontal velocity of the object at time is (b) The vertical Velocity of the object at time is (c) The tangent line to the path is horizontal at time to (d) The object crosses the y-axis at time to...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
2. Consider the parametric equations x = 5 - 12, y = 13 - 481 a. Find , and determine for what values oft is the curve concave up. and when is it concave down. 2 .- der2 b. Find where is the tangent line horizontal, and where is it vertical.
(1 pt) (A) Find the parametric equations for the line through the point P = (2, 3, 4) that is perpendicular to the plane 2x + 1 y + 3z 1 . Use 't', as your variable, t 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. X= y- (B) At what point Q does this line intersect the yz-plane?
IUIUI LULUULIV KELLSHM 15 June - 21 June / MATH 1700 - Summer 2 Let the parametric curve C be defined by x = 1 - ln(t + 4), y = 1 + In(4-1), for all – 4 < t < 4. a) [4.5] Find the equation of the line tangent to Cat = 1. b) [4.5] Does the curve C have a horizontal tangent line? If yes, find the coordinates of the point(s) at which C has horizontal tangent(s)....
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point...
6. (a) Newton's method for approximating a root of an equation f(x) 0 (see Section 3.8) can be adapted to approximating a solution of a system of equations f(x, y) 0 and gx, y) 0. The surfaces z f(x, y) and z g(x, y) intersect in a curve that intersects the xy-plane at the point (r, s), which is the solution of the system. If an initial approxi- mation (xi, yı) is close to this point, then the tangent planes...
Directions: In 7-10, determine the rectangular equation given its polar form. [7] = 9 A. x + y2 = 3 B. x + y2 = 9 C. x² + y2 = 81 D. x + y = 9 [8] r = - 179csce A. X = -179 B. x = 179 c. y = -179 D. y = 179 E. none of these [9] @ = 13 A. y =- 13 3 x B.y = c. y = -13 D....