From the question we can deduce the formula to be 16 + 3n = 76
3n - 76 - 16
3n = 60
n = 20
20 is the answer.
Answer:



Step-by-step explanation:
step 1
Find the measure of side c
Applying the law of cosines

substitute the given values



step 2
Find the measure of angle A
Applying the law of sine

substitute the given values




step 3
Find the measure of angle B
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so

substitute the given values



This is a problem of maxima and minima using derivative.
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:
Surface area of the square base =

Surface area of the rectangular sides =

Therefore, the total area of the cube is:

Isolating the variable y in terms of x:

Substituting this value in V:

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

Solving for x:

Solving for y:

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ftWidth = 4 ftHeight = 2 ftAnd its volume is: