Problem 2: Plot the LST (y?axis) corresponding
to 10:00 AM versus months (x?axis) (consider the 21st...
Problem 2: Plot the LST (y?axis) corresponding
to 10:00 AM versus months (x?axis) (consider the 21st day of each
month as the representative of each month) for Panama City Bay,
Florida.
Pendulum experiment:
1) create a plot of length (x axis) versus average period (y
axis). Make sure to clearly label your axes and indicate units.
(2) create a plot of length (x axis) versus (average period)2 (y
axis). Add a linear trend line. Record the slope of the best fit
line.
(3) recall that the period of an ideal simple pendulum is given
by the following relation: T= 2pi sq rt of L/g
squaring both sides of the equation gives...
Let R be the region enclosed by the x-axis, the y-axis, the line
x = 2 , and the curve ? = 2?? +3?
(1) Find the area of R by setting up and evaluating the
integral.
(2) Write, but do not evaluate, the volume of the solid
generated by revolving R around
the y-axis
(3) Write, but do not evaluate the volume of the solid generated
by revolving R around
the x-axis
(4) Write, but do not evaluate the...
The region bounded by y=(1/2)x, y=0, x=2 is rotated around the
x-axis.
A) find the approximation of the volume given by the right
riemann sum with n=1 using the disk method. Sketch the cylinder
that gives approximation of the volume.
B) Fine dthe approximation of the volume by the midpoint riemann
sum with n=2 using disk method. sketch the two cylinders.
Consider the region R between the x-axis and the curve y = x^3 /
3 , between x = 0 and x = 1.
(a) Calculate the surface area of the solid obtained by
revolving R about the x-axis.
(b) Write an integral for the the surface area of the solid
obtained by revolving R about the y-axis
Consider a region R bounded by the y-axis, the line
segment y=8-x for x from 0 to 8, and part of the circle
y=-sqrt(64-x^2) for x from 0 to 8. Find the centroid.
Determine the eigenvalues and the corresponding normalized
eigenfunctions of the following Sturm–Liouville problem: y''(x) +
λy(x) = 0, x ∈ [0;L], y(0) = 0, y(L) = 0,
Consider the optimization problem of the objective function f(x,
y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down
the Lagrangian function and the first-order conditions. 1 mark 2.
Determine the stationary point. 2 marks 3. Does the stationary
point represent a maximum or a minimum? Justify your answer.