A right triangle has one vertex at the origin and one vertex on the curve y=e^-x/4 for 1 ≤ x ≤ 5. One of the two perpendicular sides is along the x-axis; the other is parallel to the y -axis. Find the maximum and minimum areas for such a triangle. Round your answers to three decimal places.

14

step-by-step explanation:

the opening of this porabola is facing up

step-by-step explanation:

hope this !

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west