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Answer:
The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³
Step-by-step explanation:
From the given information;
Let a be the cost of the box
Let b be one side of the square base ; &
h to be the height of the box
We know that the volume of the box = 10 cubic feet
Then;
a²h = 10
h = 10/a²
The base = (0.65)a²
The top = (0.2)a²
The side = (0.2) a × 25/a²
= 5/a
For the four sides of the box now ;
= (0.2) 4a × 25/a²
= 0.8 × 25/a
= 20 /a
The total cost of the box is:
b = 0.65a² + 0.2a² + 20 /a
b = 0.85 a² + 20 /a
Taking differential of b with respect to a ;we have:
db/da = 1.7a - 1/a²(20) = 0
1.7 a³ - 20 = 0
1.7 a³ = 20
a³ = 20/1.7
a³ = 11.77
a =
a = 2.274 ft
Thus; the cost for the base of the box = (0.65)a²
the cost for the base of the box =(0.65) × ( 2.274)²
the cost for the base of the box = 3.362
The top of the box = (0.2)a²
The top of the box = (0.2)× ( 2.274)²
The top of the box = 1.034
The four sides of the box = 20 /a
The four sides of the box = 20/2.274
The four sides of the box = 8.795
the total cost = b = 0.85 a² + 20 /a
the total cost = 0.85 (2.274)² + 20 /2.274
the total cost = 4.395 + 8.795
the total cost = 13.19
Recall that:
the volume of the box = 10 cubic feet
Then;
a²h = 10
h = 10/a²
h = 10/ 2.274²
h 1.934
The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³
If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are
ways of picking the vowels, and
ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is
Keep in mind that this means words like TRIES and TIRES are treated as different.