# Tutor profile: Juan Manuel O.

## Questions

### Subject: Spanish

Por qué es imposible viajar al pasado?

La idea de viajar al pasado es una que ha estado en la mente de todos, sin embargo, esto es algo que jamás será posible realizar. Para explicarlo tomamos la "Paradoja de Abuelo" que consiste en que una persona al pasado y mata al padre biológico de su padre biológico (abuelo del viajero), antes de que éste conozca a la abuela del viajero y el padre del viajero pueda ser concebido. Entonces, ¿quién mato al abuelo? Uno podría decir "pero, yo no viajaría a matar a mi abuelo", sin embargo, cualquier acción que uno realice en el pasado va a desencadenar un futuro totalmente diferente al presente del que partió el viajero. Sin embargo, cabe la posibilidad de que al momento de viajar al pasado, se haya generado un futuro alternativo, uno en que el abuelo si muere y el viajero nunca nace, pero el que lo mató fue un viajero de otra línea de tiempo.

### Subject: Algebra

Solve the following polynomial equation and list all zeros for x: 3 x^2 - 2 x - 21 = 0

Here is a simple quadratic equation, as it is in the form of Ax^2+Bx+C=0 The first step we need to take to find the zeros is multiplying and dividing the polynomial by the coefficient of the first term, that is A/A. As we can see, this will not affect the result as A/A=1 and anything multiplied by 1 is the same number. (3/3)*(3 x^2 - 2 x - 21) = 0 Which after distributing the (3/3) we get (3 * 3 x^2 - 3 * 2 x - 3 * 21) / 3= 0 We operate the coefficients of the first and third terms, the middle one stays only indicated (9 x^2 - (3) * 2 x - 63) / 3 = 0 Now we need to find two numbers whose sum is B, and whose product is A*C, for the example, two numbers whose sum is 2, and whose product is 63. In this case, the two numbers are -7 and 9. As we can see the sum of them is 2 and when multiplying them we get -63. Now that we have the two numbers, we will add each one of them to each x in separate parentheses (we have two values of x since we have x^2). Note as well that The equation will be rewritten as the following: ( (3x-7*(3)) (3x+9) ) / 3 = 0 Note that the coefficient of the first term was distributed in each factor. Now we need to simplify the equation. As we can see, we can factor out the "3" from the first factor, that is ( 3*(x-7) (3x+9) ) / 3 = 0 and then rewrite the equation as (3/3)* (x-7) (3x+9) = 0. (3/3) is equal to 1 so we have (x-7) (3x+9) = 0 Now that we have our equation factored, we can then find out where the zeros are by setting both (x-7) and (3x+9) to 0. Like this: x-7=0 and 3x+9=0 Solving each for x, we will have two values of x: x=7 and x= -9/3 = -3 7 and -3 are our zeros. To prove that they are, try plugging each one back into the rewritten equation that we had! For 7, we would have (7-7)(3x+9)=0, which is (0)(3x+9)=0 and eventually 0. For -3, we would have (x-7)(-3*3+9)=0, which is (x-7)(0)=0 and eventually 0. We are done! The final answer is x=7, and x= -3.

### Subject: Macroeconomics

Why deliberately increasing the minimum wage will not give minimum wage earners a real increase in their purchase power?

When the minimum wage is increased, households have more money to spend, therefore the demand for goods increases. This increase in demand is, however, not compensated by an increase in output (production). This means that for the same amount of goods, there is now more demand. This will necessarily make firms increase the price of their goods so that the demand decreases. This is called inflation, that is the increases in the general price level. With the increase in inflation, are now the households not able to afford the products they were expecting to buy with the increase in their minimum wage because they are now more expensive. The households are found in the same situation as before, in which with their money they are only able to afford a specific amount of goods. A solution to this situation is that if a country decides to increase the minimum wage, it also has to integrate policies that increase productivity and output so that minimum wage earners are able to see a real increase in their purchase power.

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