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lara31 [8.8K]
3 years ago
10

A pastry chef has a container with 1/4 pound of sprinkles the chef needs to spread the sprinkles equally among 5 cakes. What fra

ction of the sprinkles will the chef use on each chef ?

Mathematics
1 answer:
zepelin [54]3 years ago
7 0

Answer:

d

Step-by-step explanation:

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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

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
2 years ago
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