3 years ago

What is parentheses one fourth parentheses cubed three

Mathematics

1 answer:

Anna71 [15]3 years ago

3 0

Answer:

(1/4) ^3 = 0.0833333333

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The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+

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Answer:

Total revenue = $\frac{169}{2}\ln(13)-\frac{169}{4}$ dollars

Step-by-step explanation:

$R'(x)=(x+1)\ln(x+1)$

Integrate with respect to $x$ .

$R(x)=$ ∫ $(x+1)\ln(x+1)$ dx

Take $x+1=u$

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$R(x)=$ $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u^2}{2}\frac{1}{u}\,du$

= $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u}{2}\,du$

Put $u=x+1$

$R(x)= \frac{(x+1)^2}{2}\ln(x+1)-\frac{(x+1)^2}{4}$

To find total revenue from the sale of the first 12 calculators, put $x=12$

$R(x)= \frac{(12+1)^2}{2}\ln(12+1)-\frac{(12+1)^2}{4}\\\\= \frac{(13)^2}{2}\ln(13)-\frac{(13)^2}{4}\\\\=\frac{169}{2}\ln(13)-\frac{169}{4}$

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