SPRING 2016 MATH 151 LAB ASSIGNMENT #5
DUE: MAY 3, 2016
1. Chapter #8
#11. A 20 ft-long rod is cut into 12 pieces, which are welded together to form the frame of a rectangular box. The length of the
box’s base is 15 in. longer than its width.
(a) Create a polynomial expression for the volume V in terms of x.
(b) Make a plot of V versus x.
(c) Determine the x that maximizes the volume and determine that
volume.
#12. A rectangular piece of cardboard, 40 in. long by 22 in. wide, is
used for making a rectangular box (open top) by cutting out squares
of x by x from the corners and folding up the sides.
(a) Create a polynomial expression for the volume V in terms of x.
(b) Make a plot of V versus x.
(c) Determine x if the volume of the box is 1, 000 in.3 .
(d) Determine the value of x that corresponds to the box with the
largest possible volume, and determine that volume.
#23. Growth data of a sunflower plant is given in the following table:
(a) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the
height in week 6.
In each part make a plot of the data points (circle markers) and the fitted curve.
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DUE: MAY 3, 2016
#25. The standard air density, D (average of measurements made), at different heights,
h, from sea level up to a height of 33 km is given below.
(a) Make the following four plots of the data points (density as a function of height): (1)
both axes with linear scale; (2) h with log axis, D with linear axis; (3) h with linear axis, D with log axis; (4) both log axes. According to the plots choose a function
(linear, power, exponential, or logarithmic) that best fits the data points and determine the coefficients of the function.
(b) Plot the function and the points using linear axes.
#26. Write a user-defined function that fits data points to a power function of the form
y = bxm . Name the function [b, m] = powerf it(x, y), where the input arguments x and
y are vectors with the coordinates of the data points, and the output arguments b and m
are the constants of the fitted exponential equation. Use powerfit to fit the data below.
Make a plot that shows the data points and the function.
2. Chapter #9
#4. Determine the positive roots of the equation x2 − 5x sin(3x) + 3 = 0.
SPRING 2016 MATH 151 LAB ASSIGNMENT #5
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#12. Determine the dimensions (radius r and height h) and the volume of the cylinder with the largest volume that can be made inside
of a sphere with a radius R of 14 in..
#27. The orbit of Pluto is elliptical in shape, with a = 5.9065 ×
109 km and b = 5.7208 × 109 km. The perimeter of an ellipse can be
calculated by
Z π/2 p
P = 4a
1 − k 2 sin2 θdθ
0
a2 −b2
a .
where k =
Determine the distance Pluto travels in one orbit. Calculate the average speed at which Pluto travels (in km/h) if one orbit takes about 248 years.
#32. Use a MATLAB built-in function to numerically solve:
dy
x3 e−y
= −x2 +
for 1 ≤ x ≤ 5 with y(1) = 1
dx
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Plot the solution.
#39. Tumor growth can be modeled with the equation
ν dA
A
= αA 1 −
dt
k
where A(t) is the area of the tumor and α, k, and ν are constants. Solve the equation for
0 ≤ t ≤ 30 days, given α = 0.8, k = 60, ν = 0.25, and A(0) = 1 mm2 . Make a plot of A
as a function of time.