BenoguigoliB
2020-11-08
Answered

If $2(\left({x}^{2}\right)+1)=5x$ , find $i)x-\left(\frac{1}{x}\right)ii){x}^{3}-\left(\frac{1}{{x}^{3}}\right)$

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Corben Pittman

Answered 2020-11-09
Author has **83** answers

We need to first find the value of xx by solving

To solve

Subtracting 5x5x on both sides then gives

Factoring would then gives

Now that the equation is in factored form, we can set each factor equal to 0 to find the possible values of x:

2x−1=0 \ x−2=0

2x=1 \ x=2

Now that we have the possible values of x, we can substitute them into each expression and then simplify to find the values:

If x=2, then

ii)If

If x =2, then

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Use an inverse matrix to solve system of linear equations.

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(b)

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A room can have up to 800 people. There are two types of tables: one, rectangular, seating 20 people; another, circular, that seats 9. If the organizers want to have approximately the same amount of rectangular and circular tables to seat the maximum of people possible, what combination of tables can they use?

Initially, I started off with a simple let statement, stating that $x$ will represent rectangular tables, and $y$ will represent circular tables. So my inequality so far would be something like $20x+9y\le 800$. I also know that $x\ge 0$ and $y\ge 0$. However, with this equation, I am not sure if I can actually find out an equal amount of rectangular and circular tables. I have also considered that this is a maximum/minimum problem that I have learned before, but the inequality I came up with is not a quadratic equation.

The question is multiple choice, and, substituting the correct values in, I can see that it works, but I have no idea how they arrived at the numbers. It seems to me that the question can be solved without this guess-and-check, so I'm interested in what you have to say about this problem.

Initially, I started off with a simple let statement, stating that $x$ will represent rectangular tables, and $y$ will represent circular tables. So my inequality so far would be something like $20x+9y\le 800$. I also know that $x\ge 0$ and $y\ge 0$. However, with this equation, I am not sure if I can actually find out an equal amount of rectangular and circular tables. I have also considered that this is a maximum/minimum problem that I have learned before, but the inequality I came up with is not a quadratic equation.

The question is multiple choice, and, substituting the correct values in, I can see that it works, but I have no idea how they arrived at the numbers. It seems to me that the question can be solved without this guess-and-check, so I'm interested in what you have to say about this problem.

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