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3 years ago

If a geometric sequence has a1 = 256 and a8 = 512, find the exact value of the common ratio ????.

Mathematics

1 answer:

marusya05 [52]3 years ago

7 0

Answer:r=1.104

Step-by-step explanation:

Given

First term a_1=256

$a_8=512$

Also $a_8$ can also be written in

$a_8=ar^7$

where r=common difference

$512=256r^7$

$2=r^7$

$r=\left ( 2\right )^{\frac{1}{7}}$

r=1.104

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3 years ago

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

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Answer:

The solution to the equation system given is:

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First, we must know the equations given:

2x + 3y = 1
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Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

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3 years ago