Let ℓ be the tangent line to the curve y = 2x³ at the point (1, 2). The angle of inclination of ℓ is the angle ϕ that ℓ makes with the positive direction of the x-axis.
Calculate ϕ correct to the nearest degree.

Approximately 83 degrees

Step-by-step explanation:

Consider the curve

Let us find equation of tangent or slope of tangent at (1,2)

Differentiate y wrt x

slope of tangent = value of derivative at that point

So slope of tangent at (1,2) =

Slope of a line is nothing but tangent of the angle it makes with positive x axis

So if phi is the angle

we have

Approximately 83 degrees

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2