Answer: 2/3 of an hour.
Step-by-step explanation: The constant rate of the lifeguard filling the pool is 1/3 of the pool every 1/2 hour. If she fills it for an hour, she'll get 2/3 of the pool filled. Therefore, it'll take the lifeguard 1 hour to fill the pool 2/3 of the way.
Hope this helps! :)
The number of different ways to distribute m indistinguishable balls into n
distinguishable urns is given by C(m+n-1,n-1).
For example, the number of ways 6 ball can be placed in 7 boxes is given by C(6+7-1, 7-1) = C(12, 6) = 924 ways.
Answer: 82% decrease
Step-by-step explanation:
Initial number =5000
Final number = 900
Change in numbers = 5000 - 900 = 4100
Since 5000 > 900 ( the change is a decrease)
Thus, the percent change =
(4100/5000) x 100%
= 82%
Thus, the percent of change from 5,000 to 900 is 82% decrease
You must develop a cost function C(x) and then minimize its value.
How much dwill the glass cost? It's $1 per sq ft, and the total area of the glass is 4(xh), where x is the length of one side of the base and h is the height of the tank. The area of the metal bottom is x^2, which we must multiply by $1.50 per sq ft.
This cost function will look like this: C(x) = 4($1/ft^2)xh + ($1.50/ft^2)x^2
but we know that (x^2)h= 6 cu ft, or h = (6 cu ft) / (x^2). Subst. this last result into the C(x) equation, immediately above:
C(x) = 4($1/ft^2)x[6 ft^3 / x^2] + ($1.50/ft^2)x^2
Let's focus on the numerical values and ditch the units of measurement for now:
C(x) = 4x(4/x^2) + 1.50x^2, or
C(x) = 16/x + 1.5x^2
Differentiate this with respect to x:
C '(x) = -16 / x^2 + 3 x
Set this equal to 0 and solve for x: -16/x^2 = -3x, or 16 = 3x^3
Then x^3 = 16/3, and x = 5 1/3 ft. We already have the formula
(x^2)h= 6 cu ft, so if x = 5 1/3, or 16/3, then (16/3)^2 h = 6, or
h = 6 / [16/3]^2.
h = 6 (9/256) = 0.21 ft. While possible, this h = 0.21 ft seems quite unlikely.
Please work through this problem yourself, making sure you understand each step. If questions arise, or if you find an error in my approach, please let me know.
Once again:
1. Write a formula for the total cost of the material used: 4 sides of dimensions xh each, plus 1 bottom, of dimensions x^2. Include the unit prices: $1 per square foot for the sides and $1.50 per square foot for the bottom.
2. Differentiate C(x) with respect to x.
3. Set C '(x) = 0 and solve for the critical value(s).
4. Calculate h from your value for x.
5. Write the dimensions of the tank: bottom: x^2; height: h
The question says that the line is parallel to the line above, so it is horizontal. When the line is horizontal it will be a 'Y=' Then, you take a look at the y axis and check to see what part of the axis the line is going through. Therefore, you can figure out that the awnser is C. I hope this explanation helps!
