A golden rectangle is a rectangle in which the ratio of its length to its width is equal to the ratio of the sum of its length and width to its length: L W = L + W L (values of L and W that meet this condition are said to be in the golden ratio). a. Suppose that a golden rectangle has a width of 1 unit. Solve the equation to find the exact value for the length. Then give a decimal approximation to 2 decimal places. b. To create a golden rectangle with a width of 9 ft, what should be the length? Round to 1 decimal place.
A golden rectangle is a rectangle in which the ratio of its length to its width is equal to the ratio of the sum of its length and width to its length: L W = L + W L (values of L and W that meet this condition are said to be in the golden ratio). a. Suppose that a golden rectangle has a width of 1 unit. Solve the equation to find the exact value for the length. Then give a decimal approximation to 2 decimal places. b. To create a golden rectangle with a width of 9 ft, what should be the length? Round to 1 decimal place.
Solution Summary: The author calculates the exact value of the length by solving the given equation when the golden rectangle has a width of 1 unit.
A golden rectangle is a rectangle in which the ratio of its length to its width is equal to the ratio of the sum of its length and width to its length:
L
W
=
L
+
W
L
(values of L and W that meet this condition are said to be in the golden ratio).
a. Suppose that a golden rectangle has a width of 1 unit. Solve the equation to find the exact value for the length. Then give a decimal approximation to 2 decimal places.
b. To create a golden rectangle with a width of 9 ft, what should be the length? Round to 1 decimal place.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
College Algebra with Modeling & Visualization (5th Edition)
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Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=JnLDmw3bbuw;License: Standard YouTube License, CC-BY