Answer:
The equation of the line in the slope-intercept form is:
Step-by-step explanation:
The slope-intercept form of the equation of a line is
As y intercept is -8, we have
Since the line is parallel to 
, then it has the same slope.
Let's put this equation in form and find the slope
Thus, the slope is :
Now we can finish the equation of the line in the slope-intercept form
∵ , b = -8
Therefore, the equation of the line in the slope-intercept form is:
The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.
The dimensions of your box will be 8 ft square by 4 ft high.
_____
If the base dimension is x ft, the area (quantity of material) is
... a = x² + 4x(256/x²)
... a = x² + 1024x⁻¹
Then the derivative of area with respect to x is
... a' = 2x -1024x⁻²
Setting this derivative to zero and solving for x gives the value of x for minimum area.
... 0 = 2x -1024/x²
... 512 = x³
... x = 8 . . . . . . . . same as above.
The restriction are that neither h nor g may equal zero as that would lead to division by zero.
The simplification after units cancel is:
(3(gh)^3)/100 or if you prefer
0.03(gh)^3
Answer:
14 and 4/1000 or 14004/1000
Step-by-step explanation:
1*10+3*1+4*(1/1000)
First i like to separate the equation by PEMDAS or order of operations. First is parentheses, which is the fraction. Then is exponents. There is none. Then multiplication and division so u solve 1*10, 3*1 and 4*1/1000.
This is the updated equation: 10+4+(4/1000)
Next you do subtraction and addition. The order does not matter if there's only addition. If there is subtraction u solve by the order of the equation. SO in this step we solve 10+4+(4/1000)
Here is the updated version: 14+(4/1000)
Then u add that which is 14 and 4/1000 or you can do 14004/1000
