2 years ago

Help me for this question ASAP

Mathematics

1 answer:

Ugo [173]2 years ago

6 0

Answer:

Cube

Step-by-step explanation:

The cubed root of 8 = 2 because 2³ = 8.

So 8 is perfect cube.

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What is the slope of the line that passes through the points (6,7) and (4,1)?

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2 years ago

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+

jekas [21]

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 $x+1=u$

Differentiate with respect to $x$

$dx=du$

So,

$R(x)=$ ∫ $u\ln(u)\,du$

Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx

Therefore,

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

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

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 $x=12$

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

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

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2 years ago