Determine the angle between the two lines with equations 4x - 5y = 11 and 2x + 3y = 7.

The angle between the two lines is 72.35° ⇒ to the nearest hundredth

Step-by-step explanation:

∵ The equation of the first line is 4x - 5y = 11

∴ a = 4 and b = -5

→ By using the 3rd rule of the slope above

∵ m = =

∴ m = 0.8

→ By using the 2nd rule above

∵ tan Ф = 0.8

∴ Ф = (0.8)

∴ Ф = 38.66° ⇒ to the nearest hundredth

∵ The equation of the first line is 2x + 3y = 7

∴ a = 2 and b = 3

→ By using the 3rd rule of the slope above

∵ m =

∴ m =

→ By using the 2nd rule above

∵ tan Ф =  

∴ Ф = ( )

∴ Ф = -33.69° ⇒ to the nearest hundredth

→ By using the 1st rule above

∵ Ф = -33.69 - 38.66

∴ Ф = -72.35°

→ Ignore the negative sign

∴ The angle between the two lines is 72.35° ⇒ to the nearest hundredth

V.I.N:

You can use this rule to find the angle between 2 lines tan Ф = II

(a) the volume of the cone is 20/3 in3

hence, option a is correct.