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.
Answer:
5 magdalenas
Step-by-step explanation:
Ya que vamos a estimar la cantidad de magdalenas que sobraron en la fábrica de María Magdalena. Debemos razonar como sigue.
Dado que hay el doble de magdalenas producidos en Maria Magdelena en comparación con el número producido en Font Magdelena y los magdalenas de la primera se empaquetan en dos docenas, se deduce que el número de magdalenas que quedan en Maria Magdelena sigue siendo 5 porque el número de magdalenas y el número envasado aumentó exactamente en la misma cantidad.
Perimeter = 2(l + w)
Thus,
102 = 2(l + w)
l = 6 + 2w
102 = 2( 6 + 2w + w)
102 = 12 + 4w +2 w
102 = 12 + 6w
90 = 6w
Thus, w = 15.
Length = 6 + 2w
= 6 + 30
= 36.
Thus, the length is 36 meters and width is 15 meters.
Find slope of line A:
Move into slope-intercept form y = mx+b
<span>5x + 8y = -9
8y = -5x - 9
y = (-5/8)x - 9/8
The slope of line A is -5/8.
If </span><span>Line B is perpendicular to line A, then
slope Line B = negative reciprocal of slope Line A</span>
<span>slope Line B = 8/5
So like B has the equation
y = (8/5)x + b
If it passes through (10,10), we know that when x = 10, y = 10. Use those values to solve for b:
</span>
<span>y = (8/5)x + b
10 = (8/5)·10 + b</span>
<span>10 = (8)·2 + b
10 = 16 + b
b = -6
So line B has equation </span>
<span>y = (8/5)x - 6
m = 8/5 and b = -6
so
m + b = 8/5 - 6 = 8/5 - 30/5 = -22/5
So m+b = -22/5 or -4.4 in decimal form
</span>
X= 180
now you have to multiply all them with 180
5(180)= 900
2(180)= 360
