First, square the entire problem. Then add the n's and subtract 10 from 5. You will then get 2n-5=0. Add 5 to both sides, then divide by two to get the answer. (2n=5, n=2.5)
First find the secant line. The slope of the secant line through

(when

) and

(when

) is the average rate of change of

over the interval
![[-1,2]](https://tex.z-dn.net/?f=%5B-1%2C2%5D)
:

The tangent line to

will have a slope determined by the derivative:

Both the secant and tangent will have the same slope when

, or when

.
Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
Answer:
-43 necklaces.
-total expenses=Sales=$473
Step-by-step explanation:
The breakeven point is the point where the sales revenue equals the expenditure.
-The fixed expenses is $172
-Let x be the number of necklaces sold, the breakeven point is expressed as:

Hence, Shelby has to sell 43 necklaces to breakeven.
#The expenses at the breakeven point is:

Hence, expenses at breakevent point is $473
#Sales is equal to expenses at this point, hence, sales of $473
Assuming the number is 331/2, or 331 over 2:
331/2 = 165.5 ÷ 400 = .4138 x 100% = 41.38%
100% - 41.38% = 58.62% not nickels
If the number is 33 1/2, or 33 and one half
33 1/2 = 67.5 ÷ 400 = 0.0838 x 100% = 8.38%
100% - 8.38% = 91.62% not nickels