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The first (and most typical) way to find distance of two points is by using the distance formula.
One alternative is the Manhattan metric, also called the taxicab metric. This option is much more complicated, and rarely used in high school math. d(x,y)=∑i|xi-yi|
The piece-wise linear functions can be written as follows:
.
.
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
.
When x = 5, the function is constant at -5, hence:
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
.
More can be learned about linear functions at brainly.com/question/25537936
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Area Formula:
7+10.4 x .5 x 6.7
Answer: 58.29
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