Tutor profile: Jordan A.
Translate the following sentences into Spanish: If I won a million dollars, I would buy a big house and a boat. I swear to you I will tell my boss there is a problem tomorrow. She plays the piano better than she plays the guitar.
Si ganara un millón de dólares, compraría una casa grande y un barco. Te juro que diré a mi jefe mañana que hay un problema. Ella toca el piano mejor que (ella toca) la guitarra.
You are given a sample of an unknown hydrocarbon with a mass of 10.798 grams. Total combustion of the sample yields 27.412g carbon dioxide and 14.949g water. First, determine the empirical formula of the hydrocarbon. Next, given the hydrocarbon's molecular weight of 132 grams per mole, determine the molecular formula of the hydrocarbon.
The first step to any hydrocarbon combustion analysis problem is to determine the mass of carbon and hydrogen present in the combustion products. First, let's consider the carbon dioxide, CO2. We know that the atomic weight of carbon is 12, and that of oxygen is 16. We can find the amount of carbon present by multiplying 27.412 g * (12/(12+32)), which gives us 7.476 g carbon. We repeat this with the water, H2O, with weights of 1 and 16, respectively. 14.949 g * (2/(2+16)) gives us 1.661 g H. Now, let's find the number of moles of C and H. 7.476 g C divided by 12 gives us 0.623 mol C. 1.661 g is clearly equivalent to 1.661 mol H. From here, we divide the moles of H by the moles of C, 1.661/0.623, which gives us the ratio of H to C. In this case, that ratio is approximately 2.66. When solving this type of problem, this ratio often ends up being an easily determined fraction; in this case, that fraction is 8/3. Remember, this is the ratio of H to C, so this fraction shows us the empirical formula of the compound: C3H8. Now that we have the empirical formula, we can find the molecular formula. We are given a molecular weight of 132 g/mol. Three carbons and eight hydrogens give an empirical weight of 3(12) + 8(1) = 36 + 8 = 44. Some quick division shows us that 132/4 = 3, so the carbon and hydrogen in the molecular formula are each three times that of the empirical formula. 3 * 3 = 9, and 8 * 3 = 24, so our molecular formula is C9H24.
Find the two possible solutions to the following equation: 2x^2 + 4x - 6.
There are two methods you can use to solve this problem. The first, and probably the simpler of the two, is the FOIL method. This involves some guess-and-check, but the solution can be found quickly by factoring out 2 from each term in the equation. This gives us 2(x^2 + 2x - 3). From here, we can focus on the terms inside the parentheses, making the FOIL method even easier. We find that these terms simplify to (x - 1)(x + 3). To find the roots, we set each of these new terms equal to zero and solving for x. This gives us x = 1 and x = -3. The second method is the quadratic equation. In this example, a = 2, b = 4, and c = -6. To find the first root, set up the equation x = (-4 + (4^2 - 4*2*-6)^1/2)/2*2, which simplifies to (-4 + 8)/4, which further simplifies to 1. To find the second root, we repeat the method, but we change the + to - (between the -4 and (4^2...). This simplifies to (-4 - 8)/4, which further simplifies to -3. These two roots match the roots we found using the FOIL method.
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