Consider the tangent line to the curve y = 6 sin(x) at the point (π/6, 3). (a) find a unit vector that is parallel to the tangent line to the curve at the given point.

Step-by-step explanation:

We have given the equation y = 6 sin (x)

On differentiating both side

As it passes through the point

So

Now the unit vector is parallel to the tangent so m will be 5.196

This passes through the point

So unit vector will be

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

the diver is 33 feet below the surface.

step-by-step explanation:

hope this