<h2>
Dimension of box is 2 m x 2 m x 1.33 m</h2>
Step-by-step explanation:
Let a be base side and h be the height.
Volume of box, V = a²h
The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.
That is
4a² + 3 x 4 x a x h = 48
4a² + 12 a x h = 48
a² + 3 ah = 12
![h=\frac{12-a^2}{3a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B12-a%5E2%7D%7B3a%7D)
So volume is
![V=a^2\times \frac{12-a^2}{3a}=4a-\frac{a^3}{3}](https://tex.z-dn.net/?f=V%3Da%5E2%5Ctimes%20%5Cfrac%7B12-a%5E2%7D%7B3a%7D%3D4a-%5Cfrac%7Ba%5E3%7D%7B3%7D)
At maximum volume we have derivative is zero,
![dV=4da-3\times \frac{a^2}{3}da\\\\0=4-a^2\\\\a=\pm 2](https://tex.z-dn.net/?f=dV%3D4da-3%5Ctimes%20%5Cfrac%7Ba%5E2%7D%7B3%7Dda%5C%5C%5C%5C0%3D4-a%5E2%5C%5C%5C%5Ca%3D%5Cpm%202)
Negative side is not possible, hence side of square base is 2m.
Substituting in a² + 3 ah = 12
2² + 3 x 2 x h = 12
h = 1.33 m
Dimension of box is 2 m x 2 m x 1.33 m
Answer:
The correct answer is 2 inches.
Step-by-step explanation:
Let l inches and w inches be the length and width of a rectangle respectively.
According to the given problem, l - 8 =
.
Area of the rectangle is given to be, according to the question, 18 square inches.
Thus l × w = 18
⇒ l × (2l - 16) = 18
⇒ 2
- 16l - 18 = 0
⇒
- 8l - 9 = 0
⇒ ( l - 9) ( l + 1) = 0
The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.
Width of the rectangle is 2 inches.
Answer:
12
Step-by-step explanation:
so $8.06 / .65 = 12.4 but you cannot buy .4 of a bagel so the answer would just be 12
Given expression 3² × 3⁻⁵
We will apply the power rule
![x^m*x^n=x^{m+n}](https://tex.z-dn.net/?f=x%5Em%2Ax%5En%3Dx%5E%7Bm%2Bn%7D)
3² × 3⁻⁵ = 3²⁺⁽⁻⁵⁾ = 3²⁻⁵ = 3⁻³
We will then apply the power rule
![x^{-n} = \frac{1}{x^n}](https://tex.z-dn.net/?f=x%5E%7B-n%7D%20%3D%20%20%5Cfrac%7B1%7D%7Bx%5En%7D%20)
3⁻³ =
![\frac{1}{3^3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%5E3%7D%20)
Final answer: