At hockey practice., Lars has the puck in front of the net, as shown. He is exactly 8 m away from the middle of the net, which is 2 m wide. Within what angle must Lars fire his shot in order to get it in the net, to nearest degree?

14.25°

Step-by-step explanation:

distance from middle of the net = 8 m

width of the net = 2 m

this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.

We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.

We use the trigonometric function;   tan∅ = opp/adj

opp is the side facing the angle = 1 m

adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)

adj = 8 m

tan∅ = = 0.125

∅ = 0.125 = 7.125°

Angle within which Lars must fire his shot = 2 x ∅

= 2 x 7.125° = 14.25°

answer: 20

step-by-step explanation:

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1