Answer:
Y=2x+5
Step-by-step explanation:
3 - -1
—-—— = 2=m
-1 - -3
Answer:
Required total charge is
coulombs per square meter.
Step-by-step explanation:
Given electric charge is dristributed over the disk,
so that the charge density at (x,y) is,
![\rho (x,y)=2x+2y+2x^2+2y^2](https://tex.z-dn.net/?f=%5Crho%20%28x%2Cy%29%3D2x%2B2y%2B2x%5E2%2B2y%5E2)
To find total charge on the disk let Q be the total charge and
so that,
where A is the surface of disk.
![=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA](https://tex.z-dn.net/?f=%3D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cint_%7B0%7D%5E%7B4%7D%282x%2B2y%2B2x%5E2%2B2y%5E2%29dA)
![=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta](https://tex.z-dn.net/?f=%3D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cint_%7B0%7D%5E%7B4%7D%282r%5Ccos%5Ctheta%2B2r%5Csin%5Ctheta%2B2r%5E2%20%5Ccos%5E%7B2%7D%5Ctheta%2B2r%5E2%5Csin%5E2%5Ctheta%29rdrd%5Ctheta)
![=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta](https://tex.z-dn.net/?f=%3D2%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cint_%7B0%7D%5E%7B4%7Dr%5E2%28%5Ccos%5Ctheta%2B%5Csin%5Ctheta%29drd%5Ctheta%2B2%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cint_%7B0%7D%5E%7B4%7Dr%5E3drd%5Ctheta)
![=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%7D%7B3%7D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%28%5Csin%5Ctheta%2B%5Ccos%5Ctheta%29%5CBig%5Br%5E3%5CBig%5D_%7B0%7D%5E%7B4%7Dd%5Ctheta%2B2%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5CBig%5B%5Cfrac%7Br%5E4%7D%7B4%7D%5CBig%5Dd%5Ctheta)
![=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta](https://tex.z-dn.net/?f=%3D%5Cfrac%7B128%7D%7B3%7D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%28%5Csin%5Ctheta%2B%5Ccos%5Ctheta%29d%5Ctheta%2B128%5Cint_%7B0%7D%5E%7B2%5Cpi%7Dd%5Ctheta)
![=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B128%7D%7B3%7D%5CBig%5B%5Csin%5Ctheta-%5Ccos%5Ctheta%5CBig%5D_%7B0%7D%5E%7B2%5Cpi%7D%2B128%5Ctimes%202%5Cpi)
![=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B128%7D%7B3%7D%5CBig%5B%5Csin%202%5Cpi-%5Ccos%202%5Cpi-%5Csin%200%2B%5Ccos%200%5CBig%5D%2B256%5Cpi)
Hence total charge is
coulombs per square meter.
Answer:
D.) $115
Step-by-step explanation:
9.95 x 4 = 39.8
12.95 x 2 = 25.9
15.95 x 2 = 31.9
39.8 + 25.9 + 31.9 = 97.6
97.6 x 0.18 = 17.568
97.6 + 17.568 = 115.168
115.168 ≈ 115
Answer:
Third answer (she is incorrect because she should have squared each leg length and then found the sum.)
Step-by-step explanation:
The pythagorean theorem states that a²+b²=c². This is not equivalent to (a+b)²=c² (due to FOIL expansion, this expands to a²+2ab+b²=c²).
This matches with the third answer, as she has to do a² and b≥ separately.
**This question involves expanding perfect squares, which you may wish to revise. I'm always happy to help!
False. The liter is the basic unit of volume in the metric system. The basic unit of weight is the kilogram.