Which polar coordinates represent the same point as the rectangular coordinates (-4,5)?

2nd option

Step-by-step explanation:

To convert from (x, y ) → (r, θ )

where

r =

θ = ( )

Here (x, y ) = (- 4, 5 ), a point in the 2nd quadrant

r = = =

θ = ( ) ≈ 51.3° ← related acute angle , then

θ = 180° - 51.3° = 128.7°

Thus

(- 4, 5 ) → (, 128.7° ) in polar form

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.