A 40 ft ladder leans against a building so that the top of the ladder touches the building at a point 21 ft above the ground.

To the nearest tenth of a foot, how far from the bottom of the building is the bottom of the ladder?

30.5 ft

34.0 ft

36.1 ft

42.6 ft

34.0 ft

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the distance from the bottom of the ladder to the base of the building h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

40² = 21² + h²

h² = 1600 - 441 = 1159

h = √1159 = 34 feet

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1