# Tutor profile: Callie F.

## Questions

### Subject: Basic Chemistry

How many number of moles of CO2 contains 16 g of oxygen?

We first need to figure out the mass of one mole of CO2. There are 2 oxygen molecules which means we will need to multiply oxygen's mass by 2 (16*2=32). Now we need to take Carbons mass and add it to 32. Carbon has a mass of 12 so 32+12 will give us 44grams per one mole of CO2. Now we already know that one mole of oxygen is equal to 16g. The questions wants us the give the number of moles of CO2 that contains 16g (or one mole) of oxygen. Since CO2 has 32g of oxygen we will need to divide the mass of the CO2 molecule by 2 and oxygen itself by 2. This will tell us that when CO2 has one mole of O, the mass of CO2 will become 22. Now we take 22 and divide it by 44 and we get 0.5 moles.

### Subject: Calculus

Find the derivative of 6x^4-4x^2+145

When finding derivatives there are multiple ways of doing it. The easiest way is as followed: we will take the exponent of each term and multiply it by the coefficient, and then subtract one from the exponent. So in this example, 6x^4 will turn into (4)6x^3 or 24x^3 4x^2 will turn into (2)4x^1 or 8x and 145 will become 0 because there is no x term attached to it. Therefore your final answer will be 24x^3-8x

### Subject: Algebra

Given the equation: 2(3x-1)(3x-1)=6(1-2x)-3x ; find the value of x.

The first step that will be taken with his problem is distribution. We will focus on the (3x-1)(3x-1) first, simply going left to right. When you foil this out you will get (6x^2-3x-3x+1). We will then add like terms which will give us 6x^2-6x+1. Now we have to take account of the "2" that is also being multiplied by those terms so we will distribute the 2 through and get 12X^2-12x+6. So, the left side of the equation in simplified so now lets move to the right side. Here, we will need to distribute the 6 through (1-2x) **using PEMDAS, multiplication comes before addition** and we will end up with 6-12x, now we take into account the -3x, taking 3x away from 12x (=9x). Now that we have simplified our equation to 6x^2-6x+1=(6-9x) we can start adding like terms. The 6x^2 is the only term that has an x^2 attached to it so we can leave it alone for now. We can however, move the 9x over the left side; since the 9x is negative on the right, when we carry it over to the left we are essentially adding it so (-6x)+9x turns into 3x. Treating the term "6" the same way, we will also move it to the left however this term is positive so when we carry it over to the left we will be subtracting it (1-6) which will give us -5. So, now our equation will look like: 6x^2+3x-5=0 Because our highest term is x^2 we will look at this equation as a quadratic equation. For these types of equations we will use the quadratic formula which is x= -b+/-(sqrt(b^2-4(a)(c)))/2a So by looking at this equation your "a" term will always be the coefficient attached to the x^2 term, so in this case a=6 Your "b" term will always be the coefficient attached to the "x" term which in this case will be 3 Your "c" term will always be the coefficient that has NO "x" term attached to it which in this case will be 5. Now, we will plug those values in and get x= (-3) +/- (sqrt(3^2-4(6)(-5))) / 2(6) We will end up with 2 different values because of the +/-, when we use the equation with the plus sign we will get x=.696 and when we use the negative sign we will get x=-1.196 Both of these answers are correct.

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