Find the acute angles between the curves at their points of intersection. (the angle between two curves is the angle between their tangent lines at the point of intersection. give your answers in degrees, rounding to one decimal place. enter your answers as a comma-separated list.) y = 4x2, y = 4x3

Step-by-step explanation:

Given that there are two curves

Eliminate y to get intersection as x=0,1

Thus points of intersection are (0,0) and (1,4)

Thus x axis is one tangent for both.

Next is

m1 =8 and m2 =12

Angle between the lines is

tan t =

Angle = tan inverse of 4/97

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is