The parent function is f(x)=x^2
Your function has been shifted from that equation.
The parabola is facing downward and is shifted up 5 units on the y axis.
Parameterize
![C](https://tex.z-dn.net/?f=C)
by
![\mathbf r(t)=(x(t),y(t),z(t))=(1-t)(0,5,2)+t(2,7,8)=(2t,5+2t,2+6t)](https://tex.z-dn.net/?f=%5Cmathbf%20r%28t%29%3D%28x%28t%29%2Cy%28t%29%2Cz%28t%29%29%3D%281-t%29%280%2C5%2C2%29%2Bt%282%2C7%2C8%29%3D%282t%2C5%2B2t%2C2%2B6t%29)
![\implies\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{44}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%20ds%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%7D%5C%2C%5Cmathrm%20dt%3D%5Csqrt%7B44%7D%5C%2C%5Cmathrm%20dt)
So the line integral is equivalent to
Answer:
N =10
Step-by-step explanation:
Answer:
$3185
Step-by-step explanation:
Multiply the number of grade 6 students by the money needed ($3.50) and you get 318x3.50=1113
Multiply the number of grade 7 students by the money needed ($3.50) and you get 286x3.50=1001
Multiply the number of grade 8 students by the money needed ($3.50) and you get 306x3.50=1071
Add all the total amounts together and you get $3185
0.67y + 4...when y = 2
0.67(2) + 4 = 5.34
0.67y + 4...when y = -2
0.67(-2) + 4 = 2.66