Answer:
1666.7 minutes
Step-by-step explanation:
To find out how many minutes it takes to fill the pool, you can use the formula:
Time (minutes) = Total volume / Flow rate
In this case, the total volume of the pool is 15,000 gallons, and the flow rate is 9 gallons per minute.
Time (minutes) = 15,000 gallons / 9 gallons per minute
Time (minutes) = 1,666.67 minutes (rounded to two decimal places)
So, it takes approximately 1,666.67 minutes to fill the pool.
Answer:
Step-by-step explanation:
To maximize the area of the two identical rectangular pens, we need to find the dimensions that will allow us to enclose the largest possible area using the given 480 feet of fencing.
Let's start by assigning variables to the dimensions of the rectangular pen. Let's say the length of the pen is "L" and the width is "W". Since the two pens share one wall, we can divide the available fencing equally between the two long sides and the two short sides.
The equation for the perimeter of a rectangle is: P = 2L + 2W.
In this case, we have two pens, so the total perimeter is 480 feet: 2L + 2W = 480.
We can simplify this equation by dividing both sides by 2: L + W = 240.
To maximize the area, we need to find the dimensions that satisfy this equation while maximizing the product of L and W, which represents the area.
Since the pens are identical, we can express one dimension in terms of the other. Let's solve the equation for L: L = 240 - W.
Now, substitute this expression for L in the equation for the area: A = L * W = (240 - W) * W.
To find the maximum area, we need to find the value of W that maximizes the expression (240 - W) * W.
One way to do this is by graphing the equation or using calculus, but since this is likely a high school-level problem, we can use the concept of symmetry.
Since the equation for the area is quadratic, the maximum area will occur at the midpoint of the symmetry axis. In this case, the symmetry axis is given by W = 240/2 = 120.
So, to maximize the area, each pen should have a width of 120 feet.
Substituting this value back into the equation for the perimeter, we can find the length of each pen: L + 120 = 240, L = 240 - 120 = 120.
Therefore, the dimensions of each pen that will maximize the area are 120 feet by 120 feet.
Keep in mind that this is just one possible answer, as there may be other valid dimensions that also maximize the area. However, for a symmetrical solution, both pens should have equal dimensions.
Answer:
L x W x H
Step-by-step explanation:
L=Length
W=Width
H=Height
You find your L, W, and H. Multiply your L, W, and H.
Example:
L=Length
W=Width
H=Height
L=7
W=2
H=4
7 x 2 x 4
7 x 2 = 14
14 x 4 = 56
Rearranging to check my work:
7 x 4 x 2
7 x 4 = 28
28 x 2 = 56
I was right.
Hope this answers your question.
1. The counterclockwise rotation by 90° about the origin has rule:
(x,y)→(-y,x).
Then
(-3,-1)→(1,-3).
2. Translation 4 units up has rule:
(x,y)→(x,y+4).
Then
(1,-3)→(1,1).
Answer: after composition of transformations the image point has coordinates (1,1).
Answer: Y=76 X=104 Z=104
Step-by-step explanation:
The degree 76 and y are both equal so you add it and it is 152.
Then subtract 360-152 to get 208 and since X and Z are equal you divide and get 104.