Awoman leaves home and walks 3 miles west, then 2 miles southwest. how far from home is she, and in what direction must she walk to head directly home?

North-East

Step-by-step explanation:

First she walk 3 miles west and then 2 miles southwest

i.e. she is now Southwest direction with respect to initial position

she vertically 2miles below initial position

and horizontally 3+2cos45 away from initial position

Where \theta is angle made by her with horizontal

she should walk at North of east to reach directly home

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)