Write the expression without using absolute value: |-4| if x < 4
1 answer:
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Answer:
Please check the explanation.
Step-by-step explanation:
We know that the slope or rate of change of the function can be:
- positive
- negative
- zero, or
- undefined
Function 1
From the function 1 graph, it is clear that the graph is a horizontal line. We must note that the horizontal line has a slope or rate of change zero. The reason is that the horizontal line can not rise vertically. i.e. y₂-y₁=0
so using the slope formula
Rate of change = m = y₂-y₁ / x₂-x₁
Taking two points (x₁, y₁) = (0, 4), (x₂, x₁) = (1, 4)
Rate of change = m = 4-4 / 1-0
Rate of change = m = 0/1
Rate of change = m = 0
Thus, the rate of change of function 1 is zero.
Function 2
We know the slope-intercept form of linear equation is
where m is the rate of change or slope of the function and b is the y-intercept
Given the function
comparing with the slope-intercept form i.e. y = mx+b
Therefore, the rate of change of function 2 = m = 8
Conclusion
The rate of change of function 1 = 0
The rate of change of function 2 = 8
as
- 8 - 0 = 8
Therefore, function 2 has 8 more rate of change of function than the rate of change of function 1.
So, we know both faucets open, can do the whole job in 6minutes
ok, how much has the faster cold water faucet done in 1minute then?
well, let's say the the rate of speed of the cold water faucet is "c", so in 1minute it has done 1/c of the whole work
now, we know the hot water faucet is slower, it takes it 3 times as long, that means is 1/3 the speed of the cold water faucet, so, how much does the hot water faucet do in 1min? well, we know is 1/3 fast as the cold one, the cold one is 1/c, what's 1/3 of 1/c? well, 1/3 * 1/c
now, we know they both added together, can do the whole job in 6 minutes, so in 1minute, they've done 1/6 of the job then
thus
ok, how much has the faster cold water faucet done in 1minute then?
well, let's say the the rate of speed of the cold water faucet is "c", so in 1minute it has done 1/c of the whole work
now, we know the hot water faucet is slower, it takes it 3 times as long, that means is 1/3 the speed of the cold water faucet, so, how much does the hot water faucet do in 1min? well, we know is 1/3 fast as the cold one, the cold one is 1/c, what's 1/3 of 1/c? well, 1/3 * 1/c
now, we know they both added together, can do the whole job in 6 minutes, so in 1minute, they've done 1/6 of the job then
thus