A fence 6 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. LADDER 6 ft 3 ft We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 0. L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. = (0).T [C] Once you find the value of 0 that makes L'(0) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) APR 25 E J tv

(i) sin(jx) = j sinh(x). (ii) cos(jx) = cosh(x).

in a right triangle, one of the acute angles has tan(0) Find the exact ratios (no decimals) for sin(0) and cos(0). Sketch a diagram and show your work clearly on a sheet of paper, then insert ( 2) the PNG image below (convert any format to PNG). Be sure to keep the camera in portrait mode.

Suppose that a fire truck is parked in front of a building as shown in the figure. The beacon light on top of the fire truck is located 17 feet from the wall and has a light on each side. If the beacon light rotates 1 revolution every 2 seconds, then a model for determining the distance d, in feet, that the beacon of light is from point A on the wall after t seconds is given by d(t) = 17 tan (xt). Complete parts (a) through (e) below. Explain what this means in terms of the beam of light on the wall. Choose the correct answer below. O A. When the function is undefined, the light is shining on every point on the wall. O B. When the function is undefined, the light is not shining completely on the wall. OC. When the function is undefined, there is no light shining on the wall. D. When the function is undefined, the beam of light is shining on exactly one point on the wall. (c) Fill in the following table. (d) Compute differences. 0 d(0.1)-d(0) 0.1-0 0.1 = t d(t) = 17 tan (xt)| (Type…