A woman’s height, h , is related to the length of the femur, f (the bone from the knee to the hip socket), by the formula f = 0.432 h − 10.44 . Both h and f are measured in inches. A partial skeleton is found of a woman in which the femur is 16 inches long. Police find the skeleton in an area where a woman slightly over 5 feet tall has been missing for over a year. Can the partial skeleton be that of the missing woman? Explain.
A woman’s height, h , is related to the length of the femur, f (the bone from the knee to the hip socket), by the formula f = 0.432 h − 10.44 . Both h and f are measured in inches. A partial skeleton is found of a woman in which the femur is 16 inches long. Police find the skeleton in an area where a woman slightly over 5 feet tall has been missing for over a year. Can the partial skeleton be that of the missing woman? Explain.
Solution Summary: The author calculates whether the halfway skeleton is that of the missing ladies.
A woman’s height, h, is related to the length of the femur, f (the bone from the knee to the hip socket), by the formula
f
=
0.432
h
−
10.44
. Both h and f are measured in inches. A partial skeleton is found of a woman in which the femur is 16 inches long. Police find the skeleton in an area where a woman slightly over 5 feet tall has been missing for over a year. Can the partial skeleton be that of the missing woman? Explain.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
Chapter 6 Solutions
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