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Maru [420]
3 years ago
14

olaf has 250 files on an external hard drive of those files 12% are photos.(a)write a percent proportion to find the number of f

iles that are phots.(B) how many phots does olaf have saved on his external hard drive?
Mathematics
1 answer:
Ede4ka [16]3 years ago
8 0
A) Olaf has 250 files, which represent 100%. 12% of that are photos which number is unknown (x).
250 files - 100%
x photos - 12%
So, the proportion should look like:
250 files : 100% = x : 12%

B) After crossing the products:
x = 250 files * 12% : 100%
x = 30 photos
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Using the quotient rule:
f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}
f'(x) = \frac{1 - lnx}{x^{2}}

For maximum, f'(x) = 0;
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lnx = 1, x = e

(b) <em>Deduce:
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<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
\frac{ln(e)}{e} \geq \frac{lnx}{x}
\frac{1}{e} \geq \frac{lnx}{x}, since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
\frac{x}{e} \geq lnx
x \geq elnx
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Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
e^{x} \geq e^{ln(x^{e}})
e^{x} \geq x^{e}, as required.
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