Suppose y=arctan(2x) represents our happiness at in-comex, wherexis in hundreds of thousands of dollars (for example, x = 1means income = $100,000). Use differentials to estimate our change in happi-ness when we receive a raise of $10,000 in the following scenarios: our currentincome is a) $25,000, b) $50,000, c)$500,000. Hint: Use ∆x=dx, ∆y≈dy(change in happiness is ∆y).

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

step-by-step explanation:

what are the statements? and what do you mean by "216 2 1 6"?