Question

f Dave is standing next to a silo of cross-sectional radius r = 6 feet at the indicated position, his vision will be partially obstructed. Find the portion of the y-axis that Dave cannot see. (Hint: Let a be the x-coordinate of the point where line of sight #1 is tangent to the silo; compute the slope of the line using two points (the tangent point and (12, 0)). On the other hand, compute the slope of line of sight #1 by noting it is perpendicular to a radial line through the tangency point. Set these two calculations of the slope equal and solve for a. Enter your answer using interval notation. Round your answer to three decimal places.)

Answer 1

Answer:

The answer to the following question is: 3.46

Step-by-step explanation:

Given that,

         The cross section radius = 6

          and, the tangent point = (12,0)

Let (a,b) is the point on the tangent line.

Note: b = √(36 - a^2)

The tangent line has a formula:

y = b = √(36 - a^2) * (x - 12) / (a - 12)

The Radial line slope b / a = √(36 - a^2) / a, and by perpendicularity, we know:

√(36 - a^2) / (a-12)   .   √(36 - a^2) / a = -1,

that is:

(36 - a^2) = 12a - a^2  =>  36 = 12a

then, a = 3 and b = 3√3

y = 3√3/(-18) .  (-12) = 2√3 = 3.46