Answer:
Step-by-step explanation:
15 minutes = 1/4 hour
Therefore:
75 * 4 = the number of people riding in one hour
Thus:
the # of people riding in 1 hour * 4 = the # of people riding in 4 hours
Answer:
Step-by-step explanation:
The point-slope form of an equation of a line:
m - slope
(x₁, y₁) - point
The formula of a slope:
From the table we have the points (-10, 8) and (10, 4). Substitute:
The equation of a line:
70% of 60,000,000 is 42,000,000
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
The perfect square monomial and its square root are shown in options 1, 2, and 5.
- A perfect square in mathematics is an expression that factors into two equally valid expressions. A monomial is a single phrase that is made up of the product of positive integer powers of the constants, variables, and constants. Consequently, a monomial that factors into two monomials that are the same is called a perfect square monomial.
- 1) 121, 11
- 11² = 121
- A perfect square monomial and its square root are represented by this equation.
- 2) 4x², 2x
- (2x)² = 4x²
- A perfect square monomial and its square root are represented by this equation.
- 3) 9x²-1, 3x-1
- (3x-1)² = 9x²- 6x +1
- This phrase does not depict a square monomial and its square root in perfect form.
- 4) 25x, 5x
- (5x)² = 25x²
- This phrase does not depict a square monomial and its square root in perfect form.
- 5) 49(x^4), 7x²
- (7x²)² = 49(x^4)
- A perfect square monomial and its square root are represented by this equation.
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