Title:
<h2>The revenue will be maximum for 253 passengers.</h2>
Step-by-step explanation:
Let, the number of passenger is x, which is more than 194.
In this case, the travel agency will charge [312 - (x - 194)] per passenger.
The total revenue will be ![x[312 - (x - 194)] = 506x - x^{2}](https://tex.z-dn.net/?f=x%5B312%20-%20%28x%20-%20194%29%5D%20%3D%20506x%20-%20x%5E%7B2%7D)
.
As x is the variable here, we can represent the revenue function by R(x). Hence, 
.
The revenue will be maximum when 
.
Answer:
5(2x-1) = 5(2x) - 5(1)
Step-by-step explanation:
The distributive property states that multiplying a sum or difference of two terms by a number is equal to multiplying the same number with each term of the sum or difference separately and then adding the products.
It can be written as:
a(b+c) = ab + ac
or
a(b-c) = ab - ac
So, for the given question,
=>5(2x-1) = 5(2x) - 5(1)
Answer: 2.49 gallons
Step-by-step explanation:
$32.37 divided by 13 is 2.49 :)
Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
