Find an equation of the tangent plane to the given parametric surface at the specified point.

r(u, v) = u cos vi + u sin vj + vk; u = 5, v = π/3

Equation of tangent plane to given parametric equation is:

Step-by-step explanation:

Given equation

      ---(1)

Normal vector  tangent to plane is:

Normal vector  tangent to plane is given by:

Expanding with first row

at u=5, v =π/3

                  ---(2)

at u=5, v =π/3 (1) becomes,

From above eq coordinates of r₀ can be found as:

From (2) coordinates of normal vector can be found as

Equation of tangent line can be found as:

$18 was the price of the t-shirt

step-by-step explanation:

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: