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chapter 8 (If the curve is a polygon, we can easily find its length; we…
chapter 8
If the curve is a polygon, we can easily find its length; we just add the lengths of the line segments that form the polygon. (We can use the distance formula to find the distance between the endpoints of each segment).
Thus if a smooth curve C has the equation, y = f (x), a ≤ x ≤ b let s (x) be the distance along C from the initial point P0(a, f (a)) to the point Q (x, f (x)).
The lateral surface area of a circular cylinder with radius r and height h is taken to be A = 2π rh
circular cone with base radius r and slant height l, cut it along the dashed line in Figure 2, and flatten it to form a sector of a circle with radius l and central angle θ = 2π r/l.
The fluid directly above the plate has volume V = Ad, so its mass is m = ρV = ρ Ad. The force exerted by the fluid on the plate is therefore
F = mg = ρ gAd
In general, if we have a system of n particles with masses m1, m2, . . . , mn located at the points x1, x2, . . . , xn on the x-axis, it can be shown similarly that the center of mass of the system is located at
which economists call the consumer surplus for the commodity.
which is called Poiseuille’s Law; it shows that the flux is proportional to the fourth power of the radius of the blood vessel.
Such quantities are called continuous random variables because their values actually range over an interval of real numbers, although they might be measured or recorded only to the nearest integer.
Every continuous random variable X has a probability density function f.
This means that the probability that X lies between a and b is found by integrating f from a to b:
