<span>In a three-dimensional coordinate system, the following generally points upward
</span>the positive y-axis
b is the right option
hope this helps

5 0

3 years ago

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

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

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

3 0

3 years ago

The Revenue for the week is $2000, and labor cost consists of two workers earning $8 per hour who work 40 hours each, what is la

kkurt [141]

8*40 = 320 * 2 = $640 for the 2 workers

640/2000 = 0.32

labor cost is 32% of the revenue

8 0

3 years ago

Kimberly drives at a rate of 50 miles per hour on her trip across the country. If it takes Kimberly 200 gallons of gasoline to d

ipn [44]

Answer:

Step-by-step explanation:

50 mi/hr × (1 hr / 60 min) × (200 gal / 500 mi) = ⅓ gal/min

(⅓ gal/min) × (t min) = x gal

t = 3x

3 0

3 years ago