ANSWER
![14 \: ft](https://tex.z-dn.net/?f=14%20%5C%3A%20ft)
EXPLANATION
Let the top of the hopper be
![l \: ft](https://tex.z-dn.net/?f=l%20%5C%3A%20ft)
Then, by the cosine rule,
![{l}^{2} = {13}^{2} + {15}^{2} - 2(15)(13) \cos(59.5 \degree)](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%3D%20%20%7B13%7D%5E%7B2%7D%20%20%2B%20%20%7B15%7D%5E%7B2%7D%20%20-%202%2815%29%2813%29%20%5Ccos%2859.5%20%5Cdegree%29%20)
We evaluate to get,
![{l}^{2} = 169 + 225 - 390\cos(59.5 \degree)](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%3D%20%20169%20%2B%20225%20%20%20%20-%20390%5Ccos%2859.5%20%5Cdegree%29%20)
![{l}^{2} = 394 - 197.94](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%3D%20%20394%20%20-%20197.94)
![{l}^{2} = 196.06](https://tex.z-dn.net/?f=%20%7Bl%7D%5E%7B2%7D%20%20%20%3D%20196.06)
Take positive square root of both sides to get,
![l = \sqrt{196.06}](https://tex.z-dn.net/?f=%20l%20%3D%20%20%5Csqrt%7B196.06%7D%20)
15:18 simplified is 5:6 yarrds
Four is the only number that has the same number of characters as its value in the English language
9514 1404 393
Answer:
6. x = 3
8. x = -7.5
Step-by-step explanation:
Put the number in place of the expression it is equal to, then solve for x.
__
6) g(x) = -x +5
2 = -x +5 . . . . . . . . . g(x) is replaced by 2, because g(x) = 2
x +2 = 5 . . . . . . . . . . add x to both sides
x = 3 . . . . . . . . . . . . . subtract 2 from both sides
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8) n(x) = -2x -21
-6 = -2x -21 . . . . . n(x) is replaced by its equal: -6
3 = x +10.5 . . . . . . divide both sides by -2
-7.5 = x . . . . . . . . . subtract 10.5 from both sides
_____
<em>Additional comment</em>
We have shown a couple of ways these equations can be solved. You can separate the x-term and the constant terms before you divide by the x-coefficient, or you can do it after. In the first equation, we could have solved it ...
2 -x +5
-3 = -x . . . . subtract 5
3 = x . . . . . . multiply by -1
The way we did it avoids negative numbers.
The mid-point formula can be used, which is
![(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=%28x_m%2Cy_m%29%3D%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Substitutint
(x1,y1)=(-5,3), and
(x2,y2)=(7,-1) we get