The rate of change of the distance from the particle to the origin at this instant is 3 units per second.
<h3>What is the rate of change?</h3>
The instantaneous rate of change is the rate of change at a particular instant.
A particle is moving along the curve
The rate of change of y is given as:
dy / dx = 2
by differentiating both sides,
From the question, we have:
(x, y) = (5,24)
Substitute 5 for x and dy / dx = 2
Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.
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Answer: D
Step-by-step explanation:
To find the perimeter of the square, you want to first find the length of each side. Since the figure is a square, we know that each side is equal to each other. We can set the expressions equal to each other to find x.
[subtract both sides by 1/2x]
[add both sides by 1]
[multiply both sides by 4]
Now that we know x, we can plug it into each expression to find teh length of each side.
[multiply]
[subtract]
Now that we know each side is equal to 23, we can add all the sides together to find the perimeter.
23+23+23+23=92 or 23×4=92
Since we know that the perimeter is 92 units, the answer is D.
The coefficient in (4x-2) is the -2
Step-by-step explanation:
inscribed angles subtended by the same arc are equal.
the central angle of a circle is twice any inscribed angle subtended by the same arc.
the first statement tells us that the 53° angle as well as y stay the same size no matter where on their arcs (between the 2 points connected to O) they would be. so, we don't need to bother with any line lengths.
the 2nd statement tells us that x = 2×53 = 106°. the 53° and x angles refer to the short arc on the right of the 2 points connected to O.
and y and x refer to the larger arc on the left of the 2 line connected to O. that means according to the second statement : 360-x (the big angle around O) = 2y
so,
360 - 106 = 2y
254 = 2y
y = 127°