3,400,000
I thaink but not shore if wrong i'm sorry
X=3
X/-3 = -1 ,Leave X by itself so multiply by -3 on both sides.
X = -1*-3
X = 3, negative times negative equals positive.
Answer:
6.3 cm by 6.3 cm by 12.6cm
Step-by-step explanation:
Volume of the box=![500 cm^3](https://tex.z-dn.net/?f=500%20cm%5E3)
The minimal dimensions of a box always occur when the base is a square.
![L^2H=](https://tex.z-dn.net/?f=L%5E2H%3D)
![500 cm^3](https://tex.z-dn.net/?f=500%20cm%5E3)
![H=\frac{500}{L^2}](https://tex.z-dn.net/?f=H%3D%5Cfrac%7B500%7D%7BL%5E2%7D)
Surface Area of a cylinder=![2(L^2+LH+LH)](https://tex.z-dn.net/?f=2%28L%5E2%2BLH%2BLH%29)
Surface Area of the sides and bottom= ![L^2+2(LH+LH)](https://tex.z-dn.net/?f=L%5E2%2B2%28LH%2BLH%29)
Surface Area for the top = ![L^2](https://tex.z-dn.net/?f=L%5E2)
The material for the sides and bottom costs $0.05 per ![cm^2](https://tex.z-dn.net/?f=cm%5E2)
The material for the top costs $0.15 per ![cm^2](https://tex.z-dn.net/?f=cm%5E2)
Therefore Cost of the box
![C=0.15L^2+0.05[L^2+4LH]\\C=0.2L^2+0.2LH](https://tex.z-dn.net/?f=C%3D0.15L%5E2%2B0.05%5BL%5E2%2B4LH%5D%5C%5CC%3D0.2L%5E2%2B0.2LH)
Recall:![H=\frac{500}{L^2}](https://tex.z-dn.net/?f=H%3D%5Cfrac%7B500%7D%7BL%5E2%7D)
![C=0.2L^2+0.2L(\frac{500}{L^2})\\=0.2L^2+\frac{100}{L}\\C=\frac{0.2L^3+100}{L}](https://tex.z-dn.net/?f=C%3D0.2L%5E2%2B0.2L%28%5Cfrac%7B500%7D%7BL%5E2%7D%29%5C%5C%3D0.2L%5E2%2B%5Cfrac%7B100%7D%7BL%7D%5C%5CC%3D%5Cfrac%7B0.2L%5E3%2B100%7D%7BL%7D)
The minimum value of C is at the point where the derivative is zero.
![C^{'}=\frac{2(L^3-250)}{5L^2}\\\frac{2(L^3-250)}{5L^2}=0\\2(L^3-250)=0\\L^3=250\\L=6.3cm](https://tex.z-dn.net/?f=C%5E%7B%27%7D%3D%5Cfrac%7B2%28L%5E3-250%29%7D%7B5L%5E2%7D%5C%5C%5Cfrac%7B2%28L%5E3-250%29%7D%7B5L%5E2%7D%3D0%5C%5C2%28L%5E3-250%29%3D0%5C%5CL%5E3%3D250%5C%5CL%3D6.3cm)
![H=\frac{500}{L^2}=\frac{500}{6.3^2}=12.6cm](https://tex.z-dn.net/?f=H%3D%5Cfrac%7B500%7D%7BL%5E2%7D%3D%5Cfrac%7B500%7D%7B6.3%5E2%7D%3D12.6cm)
The dimensions that would minimize the cost are 6.3 cm by 6.3 cm by 12.6cm
y = 1/2x - 2. Hope this helps
Answer:
we would need to know what the experiment was or we can't awnser