Mathematics
08.01.2020 11:50
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Jeanette obtained 32% for her statistics test, which was out of a total of 300 marks.

Jeanette obtained 32% for her statistics test, which was out of a total of 300 marks. How much should she score in the computer science test that is out of 200 marks in total if she is to get a proportionally weighted average of 46%?
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cearp
cearp
4,9(3 marks)

134

Step-by-step explanation:

So assuming x is the score on the computer science exam, it would take 300*0.32+x=500*0.46=230 to get x=134

villarrealc1987
villarrealc1987
4,7(81 marks)

The solution is  \frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] +  C

Step-by-step explanation:

From the question

    The function given is  f(x) =  \frac{e^{2x}}{ 25 + e^{4x}} dx

The  indefinite integral is  mathematically represented as

          \int\limits  {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx

Now  let  e^{2x} =  u

=>   \frac{du}{dx} 2e^{2x}

=>   2 e^{2x}dx =  du

So

\int\limits  {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx =  \int\limits  {\frac{1}{ 2(25 + u^2)} } \, du

= \frac{1}{2} \int\limits  {\frac{1}{ 25 + u^2)} } \, du

=  \frac{1}{2} \int\limits  {\frac{1}{ 5^2 + u^2)} } \, du

= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5}  +  C

Now substituting for  u

\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] +  C

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