9514 1404 393
Answer:
Step-by-step explanation:
Compare the given equation to ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
You find that k = -5, m = 1/2, h = -12.
The point is (h, k) = (-12, 5). The slope is m = 1/2.
Answer:
The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.
Step-by-step explanation:
The diagram of the situation described is shown in the attached image.
The distance of the boat to the dock along the water level at any time is x
The distance from the person on the dock to the boat at any time is y
The height of the dock is 5 ft.
These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.
According to Pythagoras' theorem
y² = x² + 5²
y² = x² + 25
(d/dt) y² = (d/dt) (x² + 5²)
2y (dy/dt) = 2x (dx/dt) + 0
2y (dy/dt) = 2x (dx/dt)
When the boat is 4 ft from dock, that is x = 4 ft,
The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s
The speed with which the boat is approaching the dock = (dx/dt)
Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock
When the boat is 4 ft from the dock, x = 4 ft.
And we can obtain y at that point.
y² = x² + 5²
y² = 4² + 5² = 16 + 25 = 41
y = 6.40 ft.
So, to the differential equation relation
2y (dy/dt) = 2x (dx/dt)
when x = 4 ft,
y = 6.40 ft
(dy/dt) = 2 ft/s
(dx/dt) = ?
2 × 6.40 × 2 = 2 × 4 × (dx/dt)
25.6 = 8 (dx/dt)
(dx/dt) = (25.6/8) = 3.20 ft/s.
Hope this Helps!!!
Answer:
Step-by-step explanation:
A linear function has the following format:
In which a is the slope(rate of change) and b is the y-intercept, that is, the value of y when x = 0.
Rate of change of 3
This means that
So
A solution at (6, 12).
This means that when x = 6, y = 12. So
The linear function is: