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Questions -
Q1. Consider the heat equation ut = kuxx defined for 0 ≤ x ≤ L with initial condition u(x, 0) = c and boundary conditions ux(0, t) = ux(L, t) = 0. Find a solution satisfying the heat equation with these initial and boundary conditions. Describe the physical meaning of the PDE and of the solution.
Q2. Consider the heat equation ut = kuxx for 0 ≤ x ≤ 1 with initial condition u(x, 0) = sin(πx) and boundary conditions u(0, t) = u(1, t) = 0. Show that u(x, t) e-kπ^2t sin(πx) is a solution. Describe the physical meaning of the PDE and of the solution.
the amplitude of a given sine function fx asinxd is 6. if the maximum value of f is 8 which is the minimum value of
an arrow is shot into the air. it's function h= 128t-16^2 find it average velocity of the arrow over the intervals from 2 seconds to 3 seconds
Maximize Z = 5 X1 + 6 X1 X2 + 2 X2Subject to: 3 X1 + 2 X2 ≥ 6X1 + X2 ≤ 8X1, X2 ≥ 0
If the rope is pulled through the pulley at a rate of 20 ft/min, at what rate will the boat be approaching the dock when 100 ft of rope is out?
What is the sample space that we use for rolling two dice, a first one and then a second one? Using this sample space.
Test the instructor claim at a 5% level of significance
The number of shark attacks and deaths over a recent 5- year period is shown. Find the mean, median, mode, midrange, variance, and standard deviation for the date. Which data set is more valuable?
A parabolic arch has a horizontal base 80 m long and the highest point is 64m above the base. Determine the height of the arch at a point 10m from either end of the base.
What is the purchase price of a 26-week "T-bill" (US Treasury note) with a maturity value of $800 that earns a simple annual interest rate of 2.0 %?
Find the value of the polynomial 8x – 6 when x = 1 and when x = –1.
What is the probability that the first marble is blue and the second is green? Write your answer as a fraction in simplest form.
a) How much will Leo receive after one year if he invests at the one-year rate?
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