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.
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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.
Let's solve this problem step-by-step.
To begin with, it is important to establish the following formula:
Angle sum of all triangles = 180°
Using this formula as well as the values of two out of three of the angles given, we can identify the value of the unknown angle as displayed as the following:
Let the unknown angle = x
Make (x) the subject as displayed as the following:
Angle sum of all triangles = 180°
180 = x + 63 + 59
x = 180 - 63 - 59
x = 58°
Therefore, the measure of each of the angles is as follows:
63°
59°
58°
M = 1 - 2 / 3 - 1
m = - 1 / 2
BD = AC Given. BD cuts AC in half. That's what bisectors do.
BD = BD Reflexive property of a line (it is always equal to itself).
<ADB = <ADC = 90o
DB is perpendicular to AC Given.
<ADB + <ADC = 180o The two are supplementary.
Each angle = 90o Perpendicular means that one line meets another at 90o
2x = 180
x = 90o
Since each of the enclosed angles = 90, two have two triangles congruent by SAS <<<< Answer
Answer:
1. Infinitely Many Solutions
2. Zero Solutions
3. One Solution ( x = 6 )
Step-by-step explanation:
1.
12x + 8 = 2( 6x + 4 )
12x + 8 = 12x + 8
2.
2( 2x + 1 ) = 4x + 3
4x + 2 = 4x + 3
2 = 3
3.
4( x + 1 ) = 3x + 10
4x + 4 = 3x + 10
x + 4 = 10
x = 6
Hopefully this helps!
Brainliest please?
