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Answer:
The percentage of the remaining alloy would become solid is 20%
Explanation:
Melting point of Cu = 1085°C
Melting point of Ni = 1455°C
At 1200°C, there is a 30% liquid and 70% solid, the weight percentage of Ni in alloy is the same that percentage of solid, then, that weight percentage is 70%.
The Ni-Cu alloy with 60% Ni and 40% Cu, and if we have the temperature of alloy > temperature of Ni > temperature of Cu, we have the follow:
60% Ni (liquid) and 40% Cu (liquid) at temperature of alloy
At solid phase with a temperature of alloy and 50% solid Cu and 50% liquid Ni, we have the follow:
40% Cu + 10% Ni in liquid phase and 50% of Ni is in solid phase.
The percentage of remaining alloy in solid is equal to
Solid = (10/50) * 100 = 20%
Answer:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12
Explanation:
A cubic has the form:
y = ax³ + bx² + cx + d
Given four points, we can write a system of equations:
1 = a + b + c + d
1/2 = 8a + 4b + 2c + d
1/3 = 27a + 9b + 3c + d
1/4 = 64a + 16b + 4c + d
Solving this algebraically would be time-consuming, but we can use matrices to make it easy.
![\left[\begin{array}{cccc}1&1&1&1\\8&4&2&1\\27&9&3&1\\64&16&4&1\end{array}\right]\left[\begin{array}{cccc}a\\b\\c\\d\end{array}\right]=\left[\begin{array}{cccc}1\\1/2\\1/3\\1/4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%261%5C%5C8%264%262%261%5C%5C27%269%263%261%5C%5C64%2616%264%261%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Da%5C%5Cb%5C%5Cc%5C%5Cd%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%5C%5C1%2F2%5C%5C1%2F3%5C%5C1%2F4%5Cend%7Barray%7D%5Cright%5D)
First, we find the inverse of the coefficient matrix. This is messy to do by hand, so let's use a calculator:
![\left[\begin{array}{cccc}1&1&1&1\\8&4&2&1\\27&9&3&1\\64&16&4&1\end{array}\right] ^{-1} =-\frac{1}{12}\left[\begin{array}{cccc}2&-6&6&-2\\-18&48&-42&12\\52&-114&84&-22\\-48&72&-48&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%261%5C%5C8%264%262%261%5C%5C27%269%263%261%5C%5C64%2616%264%261%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%20%3D-%5Cfrac%7B1%7D%7B12%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D2%26-6%266%26-2%5C%5C-18%2648%26-42%2612%5C%5C52%26-114%2684%26-22%5C%5C-48%2672%26-48%2612%5Cend%7Barray%7D%5Cright%5D)
Now we multiply by the solution matrix (again using a calculator):
![-\frac{1}{12} \left[\begin{array}{cccc}2&-6&6&-2\\-18&48&-42&12\\52&-114&84&-22\\-48&72&-48&12\end{array}\right]\left[\begin{array}{cccc}1\\1/2\\1/3\\1/4\end{array}\right] =\left[\begin{array}{cccc}-1/24\\5/12\\-35/24\\25/12\end{array}\right]](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B12%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D2%26-6%266%26-2%5C%5C-18%2648%26-42%2612%5C%5C52%26-114%2684%26-22%5C%5C-48%2672%26-48%2612%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%5C%5C1%2F2%5C%5C1%2F3%5C%5C1%2F4%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%2F24%5C%5C5%2F12%5C%5C-35%2F24%5C%5C25%2F12%5Cend%7Barray%7D%5Cright%5D)
So the cubic is:
y = -1/24 x³ + 5/12 x² − 35/24 x + 25/12
Answer:
A vehicle is considered to be legally parked if it is parked 20 feet (6 m) or more from a pedestrian crosswalk or a marked or unmarked intersection.
Explanation:
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