1/3(24x - 54) = 11(x-4)+5

Mathematics

1 answer:

fiasKO [112]3 years ago

5 0

Answer:

x = -7

Step-by-step explanation:

Step 1: Distribute

1/3(24x - 54) = 11(x - 4) + 5

8x - 18 = 11x - 44 + 5

Step 2: Solve for x

8x - 18 = 11x - 44 + 5

8x - 18 - 11x + 18 = 11x - 39 - 11x + 18

-3x / 3 = -21 / 3

x = -7

Answer: x = -7

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F(x) = lnx/x

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$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
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For maximum, f'(x) = 0;
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(b) Deduce:
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Soln: 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.