40 - 2 to the second power•9+17 can you please show me how you got this answer and tell me what it is please I will mark brainie
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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!!!
The perimeter of the kite is (10 + 2√53) units if the kite and the coordinates of the kite are point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).
<h3>What is quadrilateral?</h3>It is defined as the four-sided polygon in geometry having four edges and four corners. Kite is quadrilateral, in which. Two pairs of congruent sides, and it has one pair of opposite congruent angles.
The figure is missing.
On a coordinate plane, kite WXYZ is shown (please refer to the picture)
We have a kite and the coordinates of the kite are:
Point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).
Using the distance formula we can find the distance between coordinates:
Distance between W and X:
WX = 5 units
Similarly, distance between X and Y:
XY = √53 units
YZ = √53 units
ZW = 5 units
Perimeter = sum of the all sides
Perimeter = 5 + √53 + √53 + 5
Perimeter = (10 + 2√53) units
Thus, the perimeter of the kite is (10 + 2√53) units if the kite and the coordinates of the kite are point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).
Learn more about the quadrilateral here:
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