3 years ago

a car model comes with the following choices: 9 colors,with or without air conditioning,with or without sunroof ,with or without

automatic transmission ,with or without a spoiler,and with or without anti lock brakes. in how many ways can it be ordered

Mathematics

1 answer:

vfiekz [6]3 years ago

3 0

$9\cdot2^5=288$

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Step-by-step explanation:

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Combining like terms with rational coefficients <br> 7/8m+9/10-2m-3/5

nikklg [1K]

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Ah yes, one of my favorite topics.

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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

noname [10]

$L(x,y,z,\lambda)=10x+10y+2z+\lambda(5x^2+5y^2+2z^2-42)$

$L_x=10+10\lambda x=0\implies1+\lambda x=0$

$L_y=10+10\lambda y=0\implies1+\lambda y=0$

$L_z=2+4\lambda z=0\implies1+2\lambda z=0$

$L_\lambda=5x^2+5y^2+2z^2-42=0$

$\begin{cases}L_x=0\\L_y=0\\L_z=0\end{cases}\implies1+\lambda x=1+\lambda y=1+2\lambda z=0\implies x=y=2z$

$5x^2+5y^2+2z^2=5(2z)^2+5(2z)^2+2z^2=42z^2=42\implies z^2=1$

$z^2=1\implies z=\pm1\implies x=y=\pm2$

There are two critical points, at which we have

$f\left(2,2,1\right)=42\text{ (a maximum value)}$

$f\left(-2,-2,-1\right)=-42\text{ (a minimum value)}$

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3 years ago