Determine dy/dx in terms of t and evaluate it at the given value of t for the following parametric curves. a. x = 3 sin t, y = 2 cos t; t = pi/4b. x = 3t, y = 2t^3 ; t = 1do you just do dx/dtheta then dy/dtheta and divide dy/dtheta by dx/dtheta? then plug in value?

Step-by-step explanation:

You are correct.  dy/dx = (dy/dt) / (dx/dt)

x = 3 sin t

dx/dt = 3 cos t

y = 2 cos t

dy/dt = -2 sin t

dy/dx = (-2 sin t) / (3 cos t)

dy/dx = -⅔ tan t

t = π/4

dy/dx = -⅔ tan(π/4)

dy/dx = -⅔

  q

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1