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jeka57 [31]
2 years ago
6

Work out the volume for this prism ​

Mathematics
1 answer:
melisa1 [442]2 years ago
4 0
<h3><u>given</u><u>:</u></h3>

<u>area = 24 \:  {cm}^{2}</u>

<u>height = 8 \: cm</u>

<h3><u>to</u><u> </u><u>find</u><u>:</u></h3>

the volume of the given prism.

<h3><u>solution</u><u>:</u></h3>

<u>v = area \: of \: cross \: section \times height</u>

<u>v = 24 \times 8</u>

<u>v = 192 \:  {cm}^{3}</u>

<u>hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>prism</u><u> </u><u>is</u><u> </u><u>1</u><u>9</u><u>2</u><u> </u><u>cubic</u><u> </u><u>centimeters</u><u>.</u>

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<h2>18</h2>

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For this case we have that by definition, the density is given by:

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208.8 \ g

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Mr Smith's art class took a bus trip to an art museum. The bus averaged 65 miles per hour on the highway and 25 miles per hour i
Leya [2.2K]
Let x be the distance traveled on the highway and y the distance traveled in the city, so:
\left \{ {{x+y=375} \atop { \frac{1}{65}x+ \frac{1}{25}y =7}} \right.
 
Now, the system of equations in matrix form will be:
\left[\begin{array}{ccc}1&1&\\ \frac{1}{65} & \frac{1}{25} &\end{array}\right]   \left[\begin{array}{ccc}x&\\y&\end{array}\right] =  \left[\begin{array}{ccc}375&\\7&\end{array}\right]

Next, we are going to find the determinant:
D=  \left[\begin{array}{ccc}1&1\\ \frac{1}{65} & \frac{1}{25} \end{array}\right] =(1)( \frac{1}{25}) - (1)( \frac{1}{65} )= \frac{8}{325}
Next, we are going to find the determinant of x:
D_{x} =  \left[\begin{array}{ccc}375&1\\7& \frac{1}{25} \end{array}\right] = (375)( \frac{1}{25} )-(1)(7)=8

Now, we can find x:
x=  \frac{ D_{x} }{D} = \frac{8}{ \frac{8}{325} } =325mi

Now that we know the value of x, we can find y:
y=375-325=50mi

Remember that time equals distance over velocity; therefore, the time on the highway will be:
t_{h} = \frac{325}{65} =5hours
An the time on the city will be:
t_{c} = \frac{50}{25} =2hours

We can conclude that the bus was five hours on the highway and two hours in the city. 

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