Assuming that the equations define x and y implicitly as differentiable function
ID: 2892349 • Letter: A
Question
Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the curve x = f(t), y = g(t) at the given value of t. 2x - t^2 - t = 0, 2ty + 6t^2 = 6, t = 1 A -6 B 9 C -9 D -4 Obtain the Cartesian equation of the curve by eliminating the parameter x = 5t + 2, y = 15t + 12, -infinity lessthanorequalto t lessthanorequalto infinity A y = 3x + 6 B y = 3x - 6 C y = 3x + 12 D y = 15x + 6 Find the area of the surface generated by revolving the curves about the indicated axis. x = 6 + cos(t), y = sin(t), 0 lessthanorequalto t lessthanorequalto 2 pi; A 18 pi^2 B 6 pi^2 C 36 pi^2 D 34 pi^4 Find the area of the surface generated by revolving the curves about the indicated axis. x = sin(t), y = 6 + cos(t), 0 lessthanorequalto t lessthanorequalto 2 pi; x-axis A 24 pi^2 B 18 pi^2 C 36 pi^2 D 6 pi^2Explanation / Answer
Answer 5:
2x-t2-t = 0
Differentiating with respect to 't' :
2dx/dt -2t -1 = 0 => dx/dt = (1+ 2t)/2
2ty + 6t2 = 6
2ty = 6-6t2 => y = (6-6t2)/2t => y = 3/t - 3t
Differentiating with respect to 't' :
dy/dt = -3t-2 - 3
dy/dx = (dy/dt)/(dx/dt) => -2*(3t-2 + 3)/(1+ 2t)
Slope at t=1 => dy/dx = -2*(6)/3 = -4
Thus option D is corrrect.
Answer 6.
x = 5t+2 => t = (x-2)/5
y=15t+12 => t = (y-12)/15
equating both value of 't'
(x-2)/5 = (y-12)/15
3x - 6 = y -12
y = 3x+6
Thus answer is option A