Write and solve the differential equation that models the following verbal statement: The rate of change of Y with respect to x is proportional to 240 - x. dY = k(240– x)-r= - k(240-x)+C dx dY = k(240–x) Y= - kln(240-x)+C dx dY = k(240– x), Y= - (240-x)²+c dx dY = k(240 - x), Y= -240-x)*+C dx dY = k(240– x), Y= - In(240-x)+C dx

Explain the difference between a rate of change that is positive and one that is negative. Give an example of each. O Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with the increase in x, then the rate of change of y is positive. Whereas, if y decreases as x increases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates, the speed increases with increasing time, and the rate of change of its speed is positive. When the car brakes, the rate of change of its speed is negative, because the speed decreases over time. Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with a decrease in x, then the rate of change of y is positive. Whereas, if y decreases as x decreases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car…

In the diagram below there is a thick-walled cylindrical tube. Its height is H = 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2 = 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p x h?. R2 a) Proof that the proportionality constant k (p = kh?) is k = , ms 100m b) Determine the position of the center of mass of this object. c) Determine I, the moment of inertia of the cylindrical tube around the axle going through the center of the top (as shown on diagram). You can use lying =mr? (the rotational inertia of a ring of radius r and mass m rotating around an axis parallel to it, through its center).

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