ANSWER
307½ gallons of water
EXPLANATION
The volume of the rectangular swimming pool is
where l=25ft and w=20½ ft.
when it is filled to a depth of 4½ ft ,then the height is , h=4½ ft.
We substitute these values into the formula to get:
If one cubic foot of water is 7½ gallons, then 2306.25 cubic feet will be
We need 307.5 gallons of water to fill the pool.
See the attached image for the graph. The piecewise function is simply a collection of functions glued together to form a sort of "frankenstein function" of sorts. Here's how it works. If x is between 0 and 1 (including 0 but excluding 1), then f(x) = -2 for all x values mentioned. This is exactly what the first row of the piecewise function says. Then the second line says "if x is between 1 and 2, including both endpoints, then f(x) = 3-x". Finally the last line says f(x) = 1 as long as x is larger than 1 but smaller than 4. The value x = 4 is allowed for this piece but x = 1 is not allowed.
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Now onto function evaluation. We want to evaluate f(1) so we need to find f(x) when x = 1. If x = 1, then we'll use the second piece because the first piece excludes x = 1. So
f(x) = 3-x
f(1) = 3-1
f(1) = 2
is the first answer for the function evaluation section.
The value of f(3) is equal to 1 since we resort to using the third piece of the piecewise function (x = 3 is in the range from x = 2 to x = 4)
The value of f(-5) is undefined simply because we're out of the range defined by the piecewise function. The smallest x can get is x = 0.
Finally, f(2) is equal to 1 since...
f(x) = 3-x
f(2) = 3-2
f(2) = 1
again we use the second piece of the piecewise function because x = 2 is in the range 1 <= x <= 2
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In summary:
f(1) = 2
f(3) = 1
f(-5) = undefined
f(2) = 1
Once again have a look at the graph to see how the points match up. I've color-coded the graph so that each piece is a different color. The first piece is in red, the second in blue, the third in green. Note the open hole at point B to indicate "don't include this point as part of the graph".
Answer:
1/3 is the slope.
Step-by-step explanation:
First, we need to find the y-intercept of x + 4y = 20.
x + 4y = 20
Subtract x from both sides.
4y = -x + 20
Divide both sides by 4.
y = -1/4x + 5
Input 0 as x to find the y-intercept.
y = -1/4(0) + 5
Simplify.
y = 5
Now we know the y-intercept is (0,5). Now we need to include to find a slope that contains (0,5) and (3,6). We can use the slope formula:
(5 - 6)/(0 - 3) = m
-1/-3 = m
Simplify.
1/3 = m
1/3 is the slope.