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Scilla [17]
3 years ago
11

Need help on these problems

Mathematics
1 answer:
kupik [55]3 years ago
5 0
Simple Interest = Principal * Interest Rate * Term
Total Amount = Principal + Simple Interest

<span> <span> </span><span><span> #   Principal      Interest rate   term     Interest     Total balance
</span><span> 1 <span>         100.00         </span>6%             1 <span>           6.00 </span> <span>         106.00
</span></span><span> 3 <span>         100.00         </span>6%             2 <span>         12.00 </span> <span>         112.00
</span></span><span> 5 <span>         100.00         </span>6%             3 <span>         18.00 </span> <span>         118.00
</span></span><span> 7 <span>         100.00         </span>6%             4 <span>         24.00 </span> <span>         124.00
</span></span><span> 9 <span>      3,000.00         </span>5%             3 <span>      450.00 </span> <span>      3,450.00
</span></span><span>10 <span>     4,000.00         </span>6%             3 <span>      720.00 </span> <span>      4,720.00
</span></span><span>11 <span>   10,000.00         </span>4%             3 <span>   1,200.00 </span> <span>    11,200.00
</span></span><span>13 <span>   10,000.00         </span>6%             4 <span>   2,400.00 </span> <span>   12,400.00
</span></span><span>14 <span>   10,000.00         </span>6%             5 <span>   3,000.00 </span> <span>   13,000.00 </span> </span></span></span>
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kotegsom [21]

That's not a linear system, but you have an awesome school system for giving you this problem.

\dfrac 5 y - \dfrac 2 x = \dfrac{13}6

Multiply by 6xy to clear the fractions.

30x - 12y = 13 xy

That's a second degree equation, also known as a conic.  That one happens to be a hyperbola.  

30x = y(13 x +12)

y = \dfrac{30x}{13 x + 12}

Let's clear the fractions from the second equation, multiplying out common denominator xy:

\dfrac {36} x - \dfrac {24} y = 1

36y - 24 x = xy

We are being asked to find the meet of two hyperbolas, so we expect two answers, a quadratic equation.

Substituting,

36 \left( \dfrac{30x}{13 x + 12} \right) - 24 x = x \left( \dfrac{30x}{13 x + 12} \right)

36(30x) -24 x(13x + 12) = 30x^2

1080 x - 312 x^2- 288 x = 30x^2

x(792 - 342 x)= 0

x = 0 \textrm{ or } x=792/342 = \dfrac{44}{19}

We have to rule out x=0 because it's in the denominator.

y = \dfrac{30x}{13 x + 12} = \dfrac{30(44/19)}{13(44/19)+12}

y = \dfrac{33}{20}

Answer: (44/19, 33/20)

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