Answer:
c=40t+100
Step-by-step explanation:
Since the one-time fee to join the gym is $100, Sophia would have to pay $100 even for 0 months of membership, meaning C=\color{blue}{100}C=100 when t=\color{green}{0},t=0, which is the y-y−intercept.
(\color{green}{0}, \color{blue}{100})\text{ is a point on the graph}
(0,100) is a point on the graph
Since the total cost of membership over 5 months is $300, we know that C=\color{blue}{300}C=300 when t=\color{green}{5}.t=5.
(\color{green}{5}, \color{blue}{300})\text{ is a point on the graph}
(5,300) is a point on the graph
\text{Find the slope using the two points:}
Find the slope using the two points:
m=\frac{y_2-y_1}{x_2-x_1}=\frac{\color{blue}{300}-\color{blue}{100}}{\color{green}{5}-\color{green}{0}}=\frac{200}{5}=\color{coral}{40}
m=
x
2
−x
1
y
2
−y
1
=
5−0
300−100
=
5
200
=40
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B343%7D%7B3%7D%20%7D%20%20%5Cint%5Climits%5E7_0%20%20%5Cint%5Climits%5E%7Bx%5E2%7D_0%20%7B4x%5Csin%28y%29%7D%20%5C%2C%20dydx%20%20%3D%20-%5Cfrac%7B3%7D%7B343%7D%20%20%5Cint%5Climits%5E7_0%20%7B4x%5Ccos%28x%5E2%29%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D-%5Cfrac%7B3%7D%7B343%7D%20%5Cint%5Climits%5E%7B49%7D_0%20%7B2%5Ccos%28t%29%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%20%5Cleft%5B%5Csin%28t%29%5Cright%5D_0%5E%7B49%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%5Csin49)