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Christo W.
Chinese native speaker
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SAT
TutorMe
Question:

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)

Christo W.
Answer:

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;

Mandarin
TutorMe
Question:

Please elaborate on the difference of 的，地and得

Christo W.
Answer:

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...

Pre-Calculus
TutorMe
Question:

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

Christo W.
Answer:

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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