Answer:
9 a (5 x^2 + 3 x + 2)
Step-by-step explanation:
Simplify the following:
45 a x^2 + 27 a x + 18 a
Factor 9 a out of 45 a x^2 + 27 a x + 18 a:
Answer: 9 a (5 x^2 + 3 x + 2)
Answer: The volume of largest rectangular box is 4.5 units.
Step-by-step explanation:
Since we have given that
Volume = ![xyz](https://tex.z-dn.net/?f=xyz)
with subject to ![x+2y+3z=9](https://tex.z-dn.net/?f=x%2B2y%2B3z%3D9)
So, let ![z=\dfrac{9-x-2y}{3}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B9-x-2y%7D%7B3%7D)
So, Volume becomes,
![V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}](https://tex.z-dn.net/?f=V%3Dxyz%5C%5C%5C%5CV%3Dxy%28%5Cdfrac%7B9-x-2y%7D%7B3%7D%29%5C%5C%5C%5CV%3D%5Cdfrac%7B9xy-x%5E2y-2xy%5E2%7D%7B3%7D)
Partially derivative wrt x and y we get that
![9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9](https://tex.z-dn.net/?f=9-2x-2y%3D0%5Cimplies%202x%2B2y%3D9%5C%5C%5C%5Cand%5C%5C%5C%5C9-x-4y%3D0%5Cimplies%20x%2B4y%3D9)
By solving these two equations, we get that
![x=3,y=\dfrac{3}{2}](https://tex.z-dn.net/?f=x%3D3%2Cy%3D%5Cdfrac%7B3%7D%7B2%7D)
So, ![z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B9-x-2y%7D%7B3%7D%3D%5Cdfrac%7B9-3-3%7D%7B3%7D%3D%5Cdfrac%7B3%7D%7B3%7D%3D1)
So, Volume of largest rectangular box would be
![xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5](https://tex.z-dn.net/?f=xyz%3D3%5Ctimes%20%5Cdfrac%7B3%7D%7B2%7D%5Ctimes%201%3D%5Cdfrac%7B9%7D%7B2%7D%3D4.5)
Hence, the volume of largest rectangular box is 4.5 units.
Answer:
Step-by-step explanation:
hello :
19=3s+4
19-4 = 3s+4-4
3s=15
s=15/3
s=5
1. -6 ≤ x < -1 . . . . conjunction
2. x ≤ 6 . . or . . 10 ≤ x . . . . disjunction
3. 7 ≤ x < 12 . . . . conjunction
4. x < -9 . . or . . -3 ≤ x . . . . disjunction
5. 2 ≤ x ≤ 5 . . . . conjunction
6. x ≤ 54 . . or . . 66 ≤ x . . . . disjunction
7. 39 < x ≤ 43 . . . . conjunction
_____
Your problem statement provided no letters.
Answer:
Either B or D is the answer