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3 years ago

4. A store had 86 DVDs and 52 CDs. When the equal number of DVDs and CDs were sold,

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

3 0

Answer:

51 DVDs

Step-by-step explanation:

Let the number of DVDs and CDs sold be x each.

Initial

Number of DVDs= 86

Number of CDs= 52

After selling

Number of DVDs= 86 -x

Number of CDs= 52 -x

Given that there are 3 times as many DVDs than CDs left,

86 -x= 3(52 -x)

Expand:

86 -x= 156 -3x

Bring x terms to 1 side, constant to the other:

3x -x= 156 -86

Simplify:

2x= 70

Divide both sides by 2:

x= 35

Amount of DVDs left

= 86 -x

= 86 -35

= 51

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Step-by-step explanation:

These homogeneous recurrence relations of degree 2 have one of two solutions. Problems a, b, c, e, g have one solution; problems d and f have a slightly different solution. The solution method is similar, up to a point.

If there is a solution of the form $a[n]=r^n$ , then it will satisfy ...

$r^n=c_1\cdot r^{n-1}+c_2\cdot r^{n-2}$

Rearranging and dividing by $r^{n-2}$ , we get the quadratic ...

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We can call these values of r by the names r₁ and r₂.

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$a[n]=pr_1^n+qr_2^n$

We can find p and q by solving the initial condition equations:

$\left[\begin{array}{cc}1&1\\r_1&r_2\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]$

These have the solution ...

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And for problem (f), we get ...

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Comment on problem g

Yes, the bases of the exponential terms are conjugate irrational numbers. When the terms are evaluated, they do resolve to rational numbers.

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3 years ago