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mattsoto
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"Find the rate of chage of the distance between the origin and the moving point on the graph of y=x^2+1 if dx/dt=2 centimeters per second."...im sure it is a simple problem...any help?
The notation "dx/dt" represents the rate of change of the x-coordinate with respect to time. In other words, it measures how the x-coordinate is changing over time.
The distance from the origin to the moving point is calculated using the Pythagorean theorem, which states that the distance (d) is equal to the square root of the sum of the squares of the x-coordinate and the y-coordinate. In this case, the x-coordinate is constant (since it is given by the equation x = dx/dt * t), so the distance can be calculated by plugging in the value of y into the equation d = √(x^2 + y^2).
The constant term "1" in the equation y=x^2+1 represents the y-intercept of the parabola. It means that the parabola intersects the y-axis at the point (0,1), which is 1 unit above the origin.
As the speed (dx/dt) increases, the distance from the origin also increases. This is because the faster the point moves, the further it will be from the origin at any given time. In other words, the rate of change of the x-coordinate (dx/dt) affects the rate of change of the distance from the origin.
No, the distance from the origin is always a positive value. This is because distance is a measure of how far away a point is from a reference point, and it cannot be negative. However, the x-coordinate can be negative depending on the direction of movement of the point.