The area of the region shown in the coordinate plane is 2.7823 units square.
<h3>What is integration?</h3>
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
The graph of a function:
y = sinx
And a line segment passed through:
(0, 0) and (7π/6, -1/2)
First, find the equation of the line:
y = (-1/2)/(7π/6)[x]
y = (-3/7π)x
The area by definite integration:
![\rm Area = \int\limits^{7\pi/6}_0 {[sinx - (-3/7\pi)x]} \, dx](https://tex.z-dn.net/?f=%5Crm%20Area%20%3D%20%5Cint%5Climits%5E%7B7%5Cpi%2F6%7D_0%20%7B%5Bsinx%20-%20%28-3%2F7%5Cpi%29x%5D%7D%20%5C%2C%20dx)
![\rm Area = \int\limits^{7\pi/6}_0 {[sinx +3x/7\pi ]} \, dx](https://tex.z-dn.net/?f=%5Crm%20Area%20%3D%20%5Cint%5Climits%5E%7B7%5Cpi%2F6%7D_0%20%7B%5Bsinx%20%2B3x%2F7%5Cpi%20%5D%7D%20%5C%2C%20dx)
After solving the above definite integral:
Area = 2.7823 units square
Thus, the area of the region shown in the coordinate plane is 2.7823 units square.
Learn more about integration here:
brainly.com/question/18125359
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3 parts lemon juice and 4 parts water
3 : 4 = 0.75
<span>He mixed 0.75 parts of lemon juice with each part of water.
Hope this helps :)</span>
The equations become y=-x+4 and y=-⅔+18. Because of this, I think the graph is the one in the first attachment and the top graph.