# Tutor profile: Yujia Z.

## Questions

### Subject: TOEFL

Her *immutable* courage is crucial for her career success as a woman scientist. A. dogmatic B. flammable C. invariable D. reluctant

mut-: change --> immut-: not changing --> immutable: not changing over time. A. "dogma" is an unquestionable belief. Dogmatic describes expressions that are presented strongly as if they are true. To describe "courage" as dogmatic does not make sense. B. describe something that can cause fire. This goes out of context with the current sentence. C. var-: vary or change --> invar-: not changing. This is closet in meaning to "immutable" D. unwilling to something However, if you don't know "immutable" to start with, we can still see it's used in a positive tone to emphasize her good character. Therefore, we can eliminate dogmatic (too negative) and flammable (has nothing to do with personal qualities). "Reluctant" also goes against the context because the sentence is obviously celebrating her courage.

### Subject: C++ Programming

Given the following initializations, int i = 25; int *ptr = &i; double d = 34.7; double *ptr2 = &d; What are the values of the following? ++i; ++(*ptr); --(*ptr2)

This is what we know so far: 1. variable i and d are initialized to be 25 and 34.7, respectively 2. ptr is a pointer. But don't be caught up by this terminology. It is in essence a variable that stores the memory address of integer i; 3. ptr2, similarly, stores the address of decimal number d terminology: 1. ++(X) and --(X) mean X=X+1, X=X-1 2. * does the opposite thing as &. &X gives the memory address of X. So by contrary, *X gives the actual content stored at memory address X. answer: ++i evaluates to 25 + 1 = 26 *ptr asks for the content stored at memory address specified by ptr. We know i (not 25!) is stored in address specified by ptr. Because i has been updated to 26 in the last step, *ptr will evaluate to 26; subsequently, ++(*ptr) = 26+1 = 27 Similarly, *ptr2 asks for the content stored in address specified by ptr2, and the content is d. *ptr = 34.7. Therefore, --(*ptr2) = 34.7-1=33.7.

### Subject: Differential Equations

Find the general solution to $$\frac{dy}{dx} = 19y^2x$$

We can solve this differential equation using separation of variables. Treat x and y as individual variables. Move $$y^2$$ to the left and $$dx$$ to the right. Now we are left with $$\frac{1}{y^2}\ dy = 19x dx$$. Now take the integral on both sides, that is, $$\int \frac{1}{y^2}\ dy = \int19x dx$$ $$-\frac{1}{y} = 19\times\frac{1}{2}x^2 + C $$ (don't forget the constant for indefinite integral!) rearrange the equation to get an expression of y in terms of x $$ y = -\frac{1}{\frac{19}{2}x^2+C} $$

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