Answer:
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Step-by-step explanation:
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:
y = 
x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (6, 10) ← 2 points on the line
m = 
= 
=
The line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = x + 2 ← equation of line
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