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:
42
Step-by-step explanation:
According to ACT WorkKeys Curriculum.
To find x, you divide both sides of the equation by 12.20. This would look like this:
12.20x/12.20 =372.10/12.20 . Then, the answer you get is 30.5, so. X=30.5
Explanation: Division property of equality is dividing both sides of an equation by the same non-zero number does not change the equation.
a÷c=b÷c for c≠0
<u><em>First, you divide by 3 both sides of an equation.</em></u>
<u><em>3y/3=24/3</em></u>
<u><em>Then, simplify.</em></u>
<u><em>24/3=8</em></u>
<u><em>8*3=24</em></u>
<u><em>24/8=3</em></u>
<u><em>y=8 is the final answer.</em></u>
<u><em>Hope this helps!</em></u>
<u><em>Thanks!</em></u>
<u><em>Have a great day!</em></u>
So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!