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IgorC [24]
3 years ago
14

there are 12 students working in the library if 3/4 of them are girls how many girls are working in the library

Mathematics
2 answers:
____ [38]3 years ago
6 0
If you would like to know how many girls are working in the library, you can calculate this using the following steps:

3/4 of 12 students = 3/4 * 12 = 3 * 3 = 9 girls

Result: There are 9 girls working in the library.
navik [9.2K]3 years ago
5 0
So 3/4 of 12
remember that 12=12/1
and if you ahve x/y times z/t that equals to (xz)/(yt) so
'of' means multiply
3/4 times 12/1=(3 times 12)/(4 times 1)=36/4=9/1=9
9 are working in the library
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Employ a standard trick used in proving the chain rule:

\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h

The limit of a product is the product of limits, i.e. we can write

\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)

The rightmost limit is an exercise in differentiating \sqrt x using the definition, which you probably already know is \dfrac1{2\sqrt x}.

For the leftmost limit, we make a substitution y=\sqrt x. Now, if we make a slight change to x by adding a small number h, this propagates a similar small change in y that we'll call h', so that we can set y+h'=\sqrt{x+h}. Then as h\to0, we see that it's also the case that h'\to0 (since we fix y=\sqrt x). So we can write the remaining limit as

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which in turn is the derivative of \tan y, another limit you probably already know how to compute. We'd end up with \sec^2y, or \sec^2\sqrt x.

So we find that

\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}
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