Step-by-step explanation:
We can make 2 equations as follows:
2x = y + 16 and x + 2y = 18
x + 2y = 18 is the same as x = 18 - 2y. Hence, 2(18 - 2y) = 2x = y + 16.
2(18 - 2y) = y + 16
36 - 4y = y + 16
5y = 20
y = 4.
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Answer:
n = 12.
Step-by-step explanation:
Given:
5/6n = 10
Solve by isolating the variable. Divide both sides by 5/6. (Multiply by the reciprocal)
5/6n · 6/5 = 10 · 6/5
n = 10 · 6/5
n = 12.
Given the matrix
![\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D20%2630%5C%5C15%265%5C%5C5%262%5Cend%7Barray%7D%5Cright%5D%20)
representing the number of thousands of gallons of regular and premium oil sold by the three stations of Tiger oil company and the matrix
![\left[\begin{array}{c}500\\600\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D500%5C%5C600%5Cend%7Barray%7D%5Cright%5D%20)
representing dolloars per thousands of gallons of regular and premium oil sold by Tiger oil company.
T<span>he matrix for total dollar volume of sales using matrix multiplication is given by:
![\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right] \left[\begin{array}{c}500\\600\end{array}\right]= \left[\begin{array}{c}20(500)+30(600)\\15(500)+5(600)\\5(500)+2(600)\end{array}\right] \\ \\ = \left[\begin{array}{c}10000+18000\\7500+3000\\2500+1200\end{array}\right] =\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D20%2630%5C%5C15%265%5C%5C5%262%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D500%5C%5C600%5Cend%7Barray%7D%5Cright%5D%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D20%28500%29%2B30%28600%29%5C%5C15%28500%29%2B5%28600%29%5C%5C5%28500%29%2B2%28600%29%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D10000%2B18000%5C%5C7500%2B3000%5C%5C2500%2B1200%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D28000%5C%5C10500%5C%5C3700%5Cend%7Barray%7D%5Cright%5D)
Therefore, the total dolar </span><span>volume of sales is per thousand of gallons of oil is given by:
![\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D28000%5C%5C10500%5C%5C3700%5Cend%7Barray%7D%5Cright%5D)
</span>
The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm
Answer: (you can solve it using vertical angles, supplementary angles, and same side interior angles)