Answer: 18/80=0.225
Step-by-step explanation:
Answer:
![177 \frac{7}{9} cm^2](https://tex.z-dn.net/?f=177%20%5Cfrac%7B7%7D%7B9%7D%20cm%5E2)
Step-by-step explanation:
Length of the Plastic Sheet= 96cm
Width of the plastic Sheet =70cm
If a square of side x is cut from each corner of the plastic sheet to form the box.
Length of the box=96-2x
Width of the box=70-2x
Height of the box =x
Volume of the box = LWH
Volume=(96-2x)(70-2x)x
The maximum volume of the box is obtained at the point where the derivative is zero.
![V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)](https://tex.z-dn.net/?f=V%3D%2896-2x%29%2870-2x%29x%5C%5CV%5E%7B%27%7D%3D4%28x-42%29%283x-40%29)
Setting the derivative to 0.
![4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}](https://tex.z-dn.net/?f=4%28x-42%29%283x-40%29%3D0%5C%5Cx-42%3D0%5C%3A%203x-40%3D0%5C%5Cx%3D42%5C%3Aor%5C%3A%20x%3D%5Cfrac%7B40%7D%7B3%7D)
Since we are looking for the minimum value of x,
![x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B40%7D%7B3%7D%5C%5C%5Ctext%7BArea%20of%20the%20Square%7D%20%3D%20x%5E2%5C%5C%3D%5Cfrac%7B40%7D%7B3%7D%20X%20%5Cfrac%7B40%7D%7B3%7D%5C%5C%3D177%20%5Cfrac%7B7%7D%7B9%7D%20cm%5E2)
Answer:
9>x>-3
Step-by-step explanation:
1) first lets write 2 inequalities:
9>x and -3<x
remember -3 is less than x is the same as x is greater than -3
so I can write -3<x as
x>-3
so 9 is greater than "x" and "x" is greater than -3.....Is there any way we can combine these inequalities?
fortunately, there is a way! combing 2 inequalities as one is called a compound inequality
so 9 is greater than x:
9>x
and x is greater than -3
9>x>-3
boom!
Hope this helps!
(to solve the inequality just take the compound inequality as two seperate inequalities)
Answer:
a1 = 4
a2= -2
a3 = -8
a4= -14
a5= -20
Step-by-step explanation:
a12= a1 + 11d
-62 = 4 + 11d
-62-4 = 11d
-66= 11d
d = ![\frac{-66}{11}\\](https://tex.z-dn.net/?f=%5Cfrac%7B-66%7D%7B11%7D%5C%5C)
= -6
a1 = 4
a2 = 4 - 6 = -2
a3 = 4 - (6×2) = -8
a4 = 4 - (6×3) = -14
a5 = 4 - (6×4) = -20