What’s the distance between polar coordinates (3,−60°)and(−5,105°) ?

2 Units

Step-by-step explanation:

THere may be easier ways to do it, but I would just convert them to rectangular and find the distance between those.

(3, -60) becomes (3cos(-60), 3sin(-60)) = (3/2, -3*sqrt(3)/2)

(-5, 105) becomes (-5cos(105), -5sin(105)) = (5/2, -5sqrt(3)/2)

Now just use the distance formula, or in other words think of the two points as being connected by a horizontal and vertical line to form a right triangle.  The idea is to find the hypotenuse of that right triangle.

sqrt((3/2 - 5/2)^2 + (-3sqrt(3)/2 + 5sqrt(3)/2)^2)

sqrt((-2/2)^2 + (2*sqrt(3)/2)^2)

sqrt(1 + 3)

sqrt(4)

2

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

answer: the is put the 450

step-by-step explanation: