# Tutor profile: Mónica G.

## Questions

### Subject: Spanish

Find the error(s) in each sentence, explain it, and correct it. 1. Hola Maria! Que lindo está el dia de hoy. 2. Quiero saber cuanto costar la prenda de oro. BONUS Translate the following sentence to Spanish Tell me, is there any pasta left?

1. Hola María! Que lindo está el dia de hoy. For this sentence we have 2 mistakes, mainly focusing on the spelling of the sentence. First of all, notice the ¡ symbol is missing! In Spanish, whenver we want to use exclamation points, we must include bot at the beggining and the end of the phrase. Also, notice the word "día" is spelled incorrectly, with the accent missing. The correct spelling and grammar of the sentence would be: ¡Hola María! Que lindo está el día de hoy. 2. Quiero saber cuanto valer la prenda de oro. In this sentence we have a syntax error. The word for how much something is "worth" is "valer" or "valor", right? However, we are asking how much something is worth, so the word changes to "vale", stated in present tense to ask the value or price of something. The correct way to say the sentence would be: Quiero saber cuanto vale la prenda de oro. BONUS The correct translation would be: Dime, ¿Quedó algo de pasta?

### Subject: Calculus

Find the first derivative of the following equation: s = 4z^4 + 6z^1/2 +5z^7

We are required to find the first derivative of s = 4z^4 + 6z^1/2 +5z^7. To start with the first derivative, we must follow the derivation process, which mainly consists of: multiplying the exponent with the coefficient and subtracting 1 from the exponent. Now, I know this sounds complex, but don't worry! It's quite simple :) s = 4z^4 + 6z^1/2 + 5z^7 We have our 3 parts of the equation: 4z^4, 6z^1/2, and 5z^7 We will start with 4z^4. To derive this number, we must multiply the coefficient (4) by the exponent (4), which is 16, and that will be our new coefficient. Now for the exponent, remember I said we subtract 1? Ok, 4-1 = 3, so our new exponent will be 3, leaving us with 16z^3. Now, if we repeat this process with the other 2 parts of the equation, we will have: For 6z^1/2, 6•1/2 is 3 (our new coefficient) and for the exponent 1/2-1=-1/2, so we would have 3z^-1/2. For 5z^7 we will have 5•7 = 35 and 7-1 = 6. Therefore, 35z^6. So, for the first derivative we have: z'=16z^3 + 3z^-1/2 + 35z^6 Viola :)

### Subject: Algebra

Pablo went to the market with a $20.60 in his wallet. He purchased apples for the price of $0.50 each, bananas for $0.70 each, and watermelons for $1.60 each. He decided to buy x amount of apples, 3 more bananas than apples, and twice as many watermelons than bananas. Once he was done with the purchase, Pablo was left with only $0.10. How many apples, bananas, and watermelons did he buy?

WHAT WE NEED: amount bought of each fruit. Always keep the main goal in mind! Now, gathering up the information we know, we have that: Pablo has $20.60 Apples are $0.50 each Bananas are $0.70 each Watermelons for $1.60 each Total amount in wallet= $20.60 Total amount remaining after purchase=$0.10 Additionally, we know some information about the quantity of fruits he bought. To create a formula and display the fruit quantities, we will use the variable "x" for the amount of apples, as the rest of the quantities are based upon this number. So, apples = x We know that there are 3 more bananas than apples, which means bananas are (x+3) We know that there are twice as many watermelons, which would be 2(x+3) We know that the total money Pablo spent was the total, $20.60, minus the remainder, $0.10, which is $20.60. Ok! Now we can make our equation. The quantity of each fruit multiplied by their according prices should add up to the total amount of money spent. x(0.50) + (x+3)(0.70) + 2(x+3)(1.60) = 20.50 To solve, we must first carry on multiplication processes to have x on one side of the = sign. x(0.50) + (x+3)(0.70) + 2(x+3)(1.60) = 20.50 0.50x + 0.70x + 2.1 +3.2x + 9.6 = 20.50 our x coefficients are: 0.50, 0.70 and 3.2, so we must add them up to have a single x number. This would result in 4.4x. We must also add up the remaining numbers, 2.1 and 9.6, which add up to 11.7. 4.4x + 6.9 = 20.50 - 11.7 - 11.7 4.4x = 8.8 ----- -------- --> we need to divide by 4.4 to isolate the x 4.4 4.4 x = 2 ---> Pablo bought 2 apples. With this result we can now calculate the amount of bananas and watermelons with the previous formulas we had. Apples x = 2 apples Bananas (x+3) = 2+3 = 5 bananas Watermelons 2(x+3) = 2(2+3) = 10 watermelons In conclusion, Pablo bought 2 apples, 5 bananas, and 10 watermelons. :)

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