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Concept explainers
Heat equation The flow of hear along a thin conducting bar is governed by the one-dimensional heal equation (with analogs for thin plates in two dimensions and for solids in three dimensions)
where u is a measure of the temperature at a location x on the bar at time t and the positive constant k is related to the conductivity of the material. Show that the following functions satisfy the heal equation with k = 1.
85. u(x, t) = 4e–4t cos 2x
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Chapter 12 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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Precalculus
- Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.arrow_forwardFind the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.arrow_forward
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