# Tutor profile: Christo W.

## Questions

### Subject: SAT

If a^b = c^d, which of the following is not necessarily true? a. A^b + c^d = 2 * (a^b) b. (a^b)/(c^d) = 1 c. A = c d. A^b * c^d = a^(2*b)

The correct answer is C, as there could a million ways that give different c and d so that even a doesn't equal to c, the results could be equal; a. imagine a^b as x, and you have a^b=c^d=x; Therefore, x+x=2*x; b. Same as in a, x/x=1; d. x*x=a^(2b) a^(2b)=a^b*a^b=x*x;

### Subject: Mandarin

Please elaborate on the difference of 的，地and得

The usage of connecting grammar particles could be very subtle and complicated, but there are some basic rules to follow. As in this case, 的is typically followed by a noun, implying that what's followed by的would as an adjective; 地is usually placed before verb, suggesting that whatever that's before 地would be an adverb; 得is a bit more complicated, although it's extensively used as a pre-adverb(which is different than地since it's typically placed after adverb), it normally has the connotation of commenting at a status that's been finished. For example, 做得快 doesn't mean doing something quickly, but rather something has been done quickly; And there many more arbitrary usages of 得 that have been taken into the regular language dictions, such as 吃得了(Be able to eat up), 看的着(Be able to see)...etc...

### Subject: Pre-Calculus

Find g(x), where g(x) is the reflection across the x-axis of f(x)= -2(x–10)^2+3

1. From the ^2 we can safely conclude that this is a quadratic equation with second power being the largest power, and according to the nature of quadratic function, this function should have a parabolic shaped graph. 2. The negative - before the quadratic part of the equation implies that this function is concave down; 3. In order to get its reflection, the best way to do it is turning the original function upside down onto the other side of the axis, in this case, x-axis; By doing this, you would be changing the negative - before the quadratic part to positive +, as suggested by the characteristics of quadratic function; 4. As for the +3 at the end, it would be changed to -3, as you are turning the whole graph upside down relative to the x-axis; 5. Therefore, you get, 2(x-10)^2-3, which is the correct answer!

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