Actual length / shadow ratio is equal
Let the height of the building be x, then
36/28 = x/70
x = (36 x 70)/28 = 2,520/28 = 90.
Therefore, the height of the building is 90 feet.
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
Answer:
A. 3 * 6
Step-by-step explanation:
43 * 6 = (40 + 3) * 6 = 40 * 6 + 3 * 6
Log(k + 2k) = log60 - log4
for two functions to be equal, the arguments of each must be equal
k = 5
In order to solve for a nth term in an arithmetic sequence, we use the formula written as:
an = a1 + (n-1)d
where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.
First, we need to calculate for d from the given values above.
<span>a1 = 38 and a17 = -74
</span>
an = a1 + (n-1)d
-74 = 38 + (17-1)d
d = -7
The 27th term is calculated as follows:
a27 = a1 + (n-1)d
a27= 38 + (27-1)(-7)
a27 = -144 -----------> OPTION D
