Write a function rule for the table.
1 answer:
Answer:
p = 7.50h
Step-by-step explanation:
The answer has to be in the form of p =, since p is the pay which represents our y value, and the hours worked represents our x value. You can find the slope of the line by using the formula and any two points on the table:
That simplifies to 7.5. So the slope of the line is 7.5. We also know that the line goes through the origin (0, 0), which means, according to our data (and any data in the real world) that if you work 0 hours (x) you get 0 pay (y). So the y intercept of the line is 0. The equation, then, in slope-intercept form, is
p = 7.50h, the first choice. This means that the employee makes $7.50 per hour and should probably consider a new job.
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Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.
A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)
B. By integration, using the washer method
Volume =
![=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}](https://tex.z-dn.net/?f=%3D2%5Cpi%5Bx%5E4%2F4-2x%5E3%2F3-x%5E2%2F2%2B2x%5D_%7B-1%7D%5E%7B1%7D)
![=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])](https://tex.z-dn.net/?f=%3D2%5Cpi%28%5B1%2F4-2%2F3-1%2F2%2B2%5D-%5B1%2F4%2B2%2F3-1%2F2-2%5D%29)
= 16 π /3 as before
A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)
B. By integration, using the washer method
Volume =
= 16 π /3 as before