Answer:
The distance is minimized 22 minutes after 3:00 pm.
Step-by-step explanation:
Let t is the time for the 2 boats after 3:00 pm, we have the distance of:
- Boat 1: 20t
- Boat 2: 15t and its distance to the dock is given by (15-15t)
The paths of the boats form a right triangle, in which the hypotenuse (also the distance between the two boats) is:
D = (20t)² + (15 - 15t)²
<=> dD/dt = -2(15² )( 1-t ) +2 × 20² × t
<=> dD/dt = 2 (15² + 20²) × t -2 ( 15 )² = 0
<=> t = 2 ( 15 )² : 2 (15² + 20²)
<=> t = 0.36 hours = 0.36 × 60 = 21.6 minutes ≈ 22 minutes
Therefore, the distance is minimized 22 minutes after 3:00 pm.
Answer:
domain is all real numbers
range is y is less than or equal to 1 (it is a downward parabola)
Answer:
n=1
Step-by-step explanation:
-2(6 - 3n) + 27n = -3(n - 8)
-12+6n+27n=-3n+24
-12+33n=-3n+24
----------------------------
33n=-3n+36
+3 +3
-------------
36n=36
---- ----
n=1
