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.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
College Algebra with Modeling & Visualization (5th Edition)
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