Compare the functions below: f(x) = −3 sin(x − π) + 2
2 answers:
Given:
f(x) = - 3sin(x - π) + 2
h(x) = (x + 7)² - 1
g(x):
x: 0 1 2 3 4 5 6
g(x): 8 3 0 -1 0 3 8
For the range 0 ≤ x ≤ 6,
(a) f(x) takes a minimum value of -3 + 2 = -1, because the minimum value
for the sine function is -1.
(b) g(x) takes a minimum value of -1 according to the given table.
(c) h(x) takes a minimum value of 7^2 - 1 = 48 when x = 0.
A graph of f(x) and g(x) confirms the conclusions.
Answer: Both f(x) and g(x) have minimum values of -1.
f(x) = - 3sin(x - π) + 2
h(x) = (x + 7)² - 1
g(x):
x: 0 1 2 3 4 5 6
g(x): 8 3 0 -1 0 3 8
For the range 0 ≤ x ≤ 6,
(a) f(x) takes a minimum value of -3 + 2 = -1, because the minimum value
for the sine function is -1.
(b) g(x) takes a minimum value of -1 according to the given table.
(c) h(x) takes a minimum value of 7^2 - 1 = 48 when x = 0.
A graph of f(x) and g(x) confirms the conclusions.
Answer: Both f(x) and g(x) have minimum values of -1.
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Time taken before they are 2640 feet is 146.67 seconds
<em><u>Solution:</u></em>
The distance is given by formula:
<em><u>Ton travels at 8 feet per second</u></em>
Let us assume, time taken = t
speed = 8 feet per second
Then, distance is given as:
Distance covered by Ton = 8t
<em><u>Bob travels at 10 feet per second</u></em>
Then, distance is given as:
Distance covered by Bob = 10t
How long will it take before they are 2640 feet
Which means,
Distance covered by Ton + Distance covered by Bob = 2640
Thus time taken before they are 2640 feet is 146.67 seconds
<h3><u>Method 2:</u></h3>Since trains are moving in opposite directions, their speeds must be added
speed = 8 + 10 = 18 feet per second
Given distance = 2640 feet
Therefore, time taken is:
Thus time taken before they are 2640 feet is 146.67 seconds