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ludmilkaskok [199]
3 years ago
10

emilio build and sells homemade wooden toy for $12 each the festival he is attending charges $50 to set up his Booth how much mo

ney will he earn if he sells 32 wooden toys how much wooden toys will he still need to earn 250
Mathematics
2 answers:
LiRa [457]3 years ago
7 0

If he sells 32 it will be $384. Minus the $50 booth set up fee: $334.

He wouldnt need to sell anymore since he is over $250 after deducting the booth set up fee.

Salsk061 [2.6K]3 years ago
3 0

Emilio will earn $334.

12*32=384 --> amount of money he earns from selling

384-50 --> subtract the amount the festival charges

=334 --> final profit


<u>Please mark this answer as the Brainliest if it helped! Thank you.</u>

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\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If  $y=f(u)$  and  $u=g(x)$  then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times \dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}

\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If  $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}

\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If  $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}

Use the chain rule to differentiate the function.

\textsf{Let }\:y=u^2\:\textsf{ where }u=(x+1)

Differentiate the two parts separately:

  y=u^2 \implies \dfrac{\text{d}y}{\text{d}u}=2u

  u=x+1 \implies \dfrac{\text{d}u}{\text{d}x}=1

Put everything back into the chain rule formula:

\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =2u \times 1\\ & = 2u \\ & = 2(x+1)\\ & = 2x+2 \end{aligned}

\textsf{Therefore, }\:f'(x)=2x+2..

The <u>linear approximation</u> at a = 8 is:

\begin{aligned}L(x) & =f(a)+f'(a)(x-a)\\\\\implies L(x) & = f(8)+f'(8)(x-8)\\& = (8+1)^2+(2(8)+2)(x-8)\\& = 81+18(x-8)\\& = 18x-63\end{aligned}

Finally, substitute x = 7.8 into the <u>linear approximation equation</u>:

\begin{aligned}\implies L(7.8) & =18(7.8)-63\\& = 140.4-63\\& = 77.4\end{aligned}

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2 years ago
Read 2 more answers
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