Chapter 5: Problem 75
Define fluid pressure.
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The management at a certain factory has found that a worker can produce at most 30 units in a day. The learning curve for the number of units \(N\) produced per day after a new employee has worked \(t\) days is \(N=30\left(1-e^{k t}\right)\). After 20 days on the job, a particular worker produces 19 units. (a) Find the learning curve for this worker. (b) How many days should pass before this worker is producing 25 units per day?
In Exercises \(45-48,\) (a) use a graphing utility to graph the region bounded by the graphs of the equations, (b) explain why the area of the region is difficult to find by hand, and (c) use the integration capabilities of the graphing utility to approximate the area to four decimal places. $$ y=\sqrt{\frac{x^{3}}{4-x}}, y=0, x=3 $$
Fluid Force on a Rectangular Plate A rectangular plate of height \(h\) feet and base \(b\) feet is submerged vertically in a tank of fluid that weighs \(w\) pounds per cubic foot. The center is \(k\) feet below the surface of the fluid, where \(h \leq k / 2\). Show that the fluid force on the surface of the plate is \(\boldsymbol{F}=w k h b\)
The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$ \int_{-\pi / 3}^{\pi / 3}(2-\sec x) d x $$
(a) use a graphing utility to graph the region bounded by the graphs of the equations, \((b)\) find the area of the region, and (c) use the integration capabilities of the graphing utility to verify your results. $$ f(x)=x^{4}-4 x^{2}, \quad g(x)=x^{2}-4 $$
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