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Fudgin [204]
4 years ago
5

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2

Mathematics
1 answer:
motikmotik4 years ago
6 0
Let x =lenght, y = width, and z =height 
<span>The volume of the box is equal to V = xyz </span>
<span>Subject to the surface area </span>
<span>S = 2xy + 2xz + 2yz = 64 </span>
<span>= 2(xy + xz + yz) </span>
<span>= 2[xy + x(64/xy) + y(64/xy)] </span>
<span>S(x,y)= 2(xy + 64/y + 64/x) </span>
<span>Then </span>
<span>Mx(x, y) = y = 64/x^2 </span>
<span>My(x, y) = x = 64/y^2 </span>
<span>y^2 = 64/x </span>
<span>(64/x^2)^2 = 64 </span>
<span>4096/x^4 = 64/x </span>
<span>x^3 = 4096/64 </span>
<span>x^3 = 64 </span>
<span>x = 4 </span>
<span>y = 64/x^2 </span>
<span>y = 4 </span>
<span>z= 64/yx </span>
<span>z= 64/16 </span>
<span>z = 4 </span>

<span>Therefor the dimensions are cube 4.</span>
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Department s had 500 units 60% completed in process at the beginning of the period; 9,000 units completed during the period; and
Delicious77 [7]

With the concept of first in, first out method, then we can use the formula below to solve for the number of equivalent units of production for that period.

 

number of equivalent units of production

= Total number of units completed during that period (A) – Number of units completed in process at the beginning of the period (B) + Number of units completed at the end of the period (C)

= A – B + C

We know that,

A = 9000 units

So we solve for B and C.

B is 60% of the 500 units, therefore:

B = 0.60 * 500 = 300

C is 30% of the 600 units, therefore:

C = 0.30 * 600 = 180

 

Substituting the values into the equation:

number of equivalent units of production  = 9000 – 300 + 180

number of equivalent units of production  = 8880 units

 

Answer:

A. 8880

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