Answer:
2x
Step-by-step explanation:
f(x)- g(x)
=5x-3-(3x-3)
=5x-3-3x+3
=2x
The next 18 days because your trying to see how many days it is until he does BOTH
Answer:
w= -1
Step-by-step explanation:
Use PEMDAS to solve.
9(1 + w) - 5w = 5
distribute 9 to everything inside the parentheses.
9 x 1 = 9
9 x w = 9w
rewrite equation
9 + 9w - 5w = 5
combine like terms
9w - 5w = 4w
rewrite equation
9 + 4w = 5
subtract 9 from both sides
9 - 9 = 0
5 - 9 = -4
rewrite equation
4w = -4
divide by 4 on both sides to get w by itself.
4w / 4 = w
-4 / 4 = -1
<u>Hope This Helps :)</u>
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
L think that the answer is A-Rises Falls