Depends on the prism!
Here are the basic ones:
SA of rectangular prism = 2lw + 2wh + 2lh OR 2(lw+wh+lh)
SA of triangular prism = 2*area of base + perimeter of base*height
Answer:
The coordinate of the wells are
![(-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})](https://tex.z-dn.net/?f=%20%28-4%20-%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%2C%2070%2B15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%29)
![(-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})](https://tex.z-dn.net/?f=%20%28-4%20%2B%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%2C%2070-15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D%29)
Step-by-step explanation:
The y coordinate of the stream is given by 
. Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation
or equivalently
(by summing 15x and substracting 10 on both sides)
Dividing by 2 on both sides, we get
Recall that given the equation of the form 
the solutions are
![x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Taking a =2, b = 16 and c = -21, we get the solutions
![x_1 = -4 -\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=x_1%20%3D%20-4%20-%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
![x_2 = -4 +\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=x_2%20%3D%20-4%20%2B%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
If we replace this values in any of the equations, we get
![y_1 = 70+15\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=y_1%20%3D%2070%2B15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
![y_2 = 70-15\sqrt[]{\frac{53}{2}}](https://tex.z-dn.net/?f=y_2%20%3D%2070-15%5Csqrt%5B%5D%7B%5Cfrac%7B53%7D%7B2%7D%7D)
Answer:
Always
Step-by-step explanation: because I did it and got the answer right
