Liz W.

Engineering Undergraduate Tutor

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Basic Chemistry

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Question:

How many grams of $$O_2$$ are there in 123.58 mol of $$CO_2$$?

Liz W.

Answer:

You will first want to find the molar masses of $$O_2$$ (oxygen). Locating your periodic table, oxygen's molar mass is $$32.00 \frac{g} {mol}$$. In order to calculate the mass of $$O_2$$ in the mixture of $$CO_2$$, you must multiply the molar mass of oxygen by the moles of your substances. It will look something like this, $$123.58 \text{ mol} \times 32.00 \frac{g} {mol}$$. Your moles cancel out and you are left with about $$3,955 \text { g of } O_2$$.

Calculus

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Question:

Let $$f(x) =4x^3-5x+3$$. Find the equation of the line tangent to the graph of $$f$$ at $$x = -1$$.

Liz W.

Answer:

Your first step will be to find the first derivative of $$f(x) =4x^3-5x+3$$. Which is $$f'(x)=12x^2-5$$. You then want to find the value of $$f(x) =4x^3-5x+3$$ when $$x = -1$$, which will give you the point on the curve when $$x = -1$$. To do that, you need to solve $$f(-1) =4x^3-5x+3$$. You then plug $$-1$$ in for every $$x$$ and solve. You end up with $$f(-1) = 4$$, so your point would be $$(-1,4)$$. You then need to solve for the slope of the line and to do that, you need to solve the first derivative, $$f'(x) =12x^2-5$$, when $$x = -1$$. Your set up should look something like this $$f'(-1) =12(-1)^2-5$$ which gives you $$f'(-1) = 7$$. You have now found your slope. Then, use the point-slope formula to write the equation for the tangent line at the given x-value. Point-slope formula is $$y_2-y_1 = m (x_2-x_1)$$. When you plug in your points and your slope, your set up should look something like this: $$y-4 = 7(x- (-1))$$. Solving for $$y$$, you get $$y=7x+11$$ as the equation for the line tangent to the graph of $$f$$ at $$x=-1$$.

Algebra

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Question:

Solve -32x + 8y + 40 = 0 for y.

Liz W.

Answer:

First, you want to get the y variable by itself. Start off by adding 32x to both sides, this will eliminate -32x from the left side. Then subtract 40 from both sides, this will eliminate the + 40 from the left side. You should now be left with 8y = 32x - 40; in order to solve for y at this point, you need to divide both sides by 8, eliminating the 8y from the left side and leaving you with y = 4y - 5.

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