The function f ( x ) = 6.5 x 2 − 20.4 x + 234 x 2 + 36 models the pH level, f(x), of the human mouth x minutes after a person eats food containing sugar. The graph of this function is shown in the figure. a. Use the graph to obtain a reasonable estimate, to the nearest tenth, of the pH level of the human mouth 42 minutes after a person eats food containing sugar. b. After eating sugar, when is the pH level the lowest? Use the function's equation to determine the pH level, to the nearest tenth, at this time. c. According to the graph, what is the normal pH level of the human mouth? d . What is the equation of the horizontal asymptote associated with this function? Describe what this means in terms of the mouth's pH level over time. e. Use the graph to describe what happens to the pH level during the first hour.
The function f ( x ) = 6.5 x 2 − 20.4 x + 234 x 2 + 36 models the pH level, f(x), of the human mouth x minutes after a person eats food containing sugar. The graph of this function is shown in the figure. a. Use the graph to obtain a reasonable estimate, to the nearest tenth, of the pH level of the human mouth 42 minutes after a person eats food containing sugar. b. After eating sugar, when is the pH level the lowest? Use the function's equation to determine the pH level, to the nearest tenth, at this time. c. According to the graph, what is the normal pH level of the human mouth? d . What is the equation of the horizontal asymptote associated with this function? Describe what this means in terms of the mouth's pH level over time. e. Use the graph to describe what happens to the pH level during the first hour.
Solution Summary: The author explains how the pH level of the human mouth 42 minutes after eating food containing sugar is 6.0.
models the pH level, f(x), of the human mouth x minutes after a person eats food containing sugar. The graph of this function is shown in the figure.
a. Use the graph to obtain a reasonable estimate, to the nearest tenth, of the pH level of the human mouth 42 minutes after a person eats food containing sugar.
b. After eating sugar, when is the pH level the lowest? Use the function's equation to determine the pH level, to the nearest tenth, at this time.
c. According to the graph, what is the normal pH level of the human mouth?
d. What is the equation of the horizontal asymptote associated with this function? Describe what this means in terms of the mouth's pH level over time.
e. Use the graph to describe what happens to the pH level during the first hour.
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
Chapter 2 Solutions
Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)
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