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Reid B.
Junior Chemical Engineering Student at Texas A&M University
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Chemistry
TutorMe
Question:

How much heat ($$Q$$) does it take to raise the temperature of 40 grams of water from 20 degrees Celsius to 90 degrees Celsius? Assume that the heat capacity of water is equal to $$4.18\frac{J}{gC}$$

Reid B.

Using the equation $$Q=mC \Delta T$$ $$\Delta T=90-20=70$$ so $$Q=11704$$ Joules

Calculus
TutorMe
Question:

Find the derivative ($$y'$$) of: $$y=(x^2)*ln(x)+\frac{x^2}{ln(x)}$$

Reid B.

1) Take the derivative of the first term using the product rule: $$\frac{d}{dx}x^2ln(x)=2xln(x)+x^2\frac{1}{x}$$ 2)Take the derivative of the second term using the quotient rule: $$\frac{d}{dx}\frac{x^2}{ln(x)}=\frac{2xln(x)-x^2\frac{1}{x}}{(ln(x))^2}$$ 3)Simplify and add these 2 terms together to get the answer: $$y'=2xln(x)+x+\frac{2xln(x)-x}{(ln(x))^2}$$

Algebra
TutorMe
Question:

Solve the following equation for y and give both the slope and y-intercept of the line for the solved equation: $$14x^2+13xy=17x$$

Reid B.

1) Subtract both sides by $$14x^2$$ 2)Divide both sides of the equation by $$13x$$ 3)Cancel the x in both the expressions on the right side of the equation solved equation: $$y= \frac{-14}{13}x+\frac{17}{13}$$ The equation is now in the form of: $$y=mx+b$$ (slope-intercept form) In this form the m represents the slope and is found to be: $$\frac{-14}{13}$$ Also in this form, the b represent the y-intercept which is found to be: $$\frac{17}{13}$$

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