6x>-25 and 9x<54the answer (solve x ) you have 6x>-25 so we solve 'x' we say divide by 6 both side then we get { x>-25/6 or x>-4.166} second you have 9x<54 we say divide by 9 each side { x<6 } your answer is { x>-25/6 and x<6 }

7 0

3 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

4 0

3 years ago

A small half bath measures 42 inches by 48 inches.What is the square footage of the half bath?

Mkey [24]

A=LW, we are told that the dimensions are 42 and 48 so:

A=42*48

A=2016in^2

3 0

3 years ago

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