Answer:
A stack is an ordered list of elements where all insertions and deletions are made at the same end, whereas a queue is exactly the opposite of a stack.
Explanation:
Answer:
simple projects bovonhztisgx
Answer:
Explanation:
The explanations and answers are shown in the following attachments
Answer:
Space mean speed = 44 mi/h
Explanation:
Using Greenshield's linear model
q = Uf ( D -
/Dj )
qcap = capacity flow that gives Dcap
Dcap = Dj/2
qcap = Uf. Dj/4
Where
U = space mean speed
Uf = free flow speed
D = density
Dj = jam density
now,
Dj = 4 × 3300/55
= 240v/h
q = Dj ( U -
/Uf)
2100 = 240 ( U -
/55)
Solve for U
U = 44m/h
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