# Tutor profile: Marjana I.

## Questions

### Subject: Pre-Calculus

Simplify the expression $\log_4 \frac{36}{5}+\log_4 \frac{10}{9}$.

$\log_4 \frac{36}{5}+\log_4 \frac{10}{9}$ $=\log_4(36/5)(10/9)=\log_4 8=3/2$ since $4^{3/2}=(\sqrt{4})^3=2^3=8$.

### Subject: Calculus

True or False. If F(x) = ∫ -23x sin(t) dt then the second fundamental theorem of calculus can be used to evaluate F '(x) as follows F '(x) = sin (3x)

False. Note that the upper limit in the integral above is 3x and not x, hence the integral above has the form F(x) = ∫ -2u(x) f(t) dt Using the chain rule, we can write F '(x) = dF / du * du / dx = 3 sin (3x)

### Subject: Algebra

After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian had answered 150 questions correctly, how many correct answers did he answer in the second test? a. 105 b. 120 c. 180 d. 195

The answer is choice D The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so, 150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100 so 150 + 45 = 195

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