In cutting down a tree of radius 24 inches, a notch is made, one face of which is horizontal and the other inclined to the first at an angle of 60 degrees. if the edge of the notch passes through the center of the tree, find the volume of wood cut out in making the notch.

about 15,962.6 cubic inches

Step-by-step explanation:

The formula for the volume of a cylindrical wedge with its edge a diameter is ...

V = (2/3)h·r^2

Since the cut is at a 60° angle, the height of the opening is ...

(24 in)·tan(60°) ≈ 41.56922 in

Then the volume is ...

V = (2/3)(41.56922 in)(24 in)^2 ≈ 15,962.8 in^3

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18