Acircular pool measures 88 feet across. one cubic yard of concrete is to be used to create a circular border of uniform width around the pool. if the border is to have a depth of 3 inches, how wide will the border be?

  4.667 inches

Step-by-step explanation:

The volume of the border is the product of its area and depth. Its area is the product of its width and the length of its centerline.

If x is the width of the border in feet, the diameter of its centerline is ...

  d = 88+x

Then the circumference of that circle, the length of the centerline, is ...

  C = πd = π(88+x)

and the area is the product of this length and the width of the border:

  A = xC = πx(88+x)

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The depth is expected to be 3 inches, or 1/4 foot, and the volume is (3 ft)³ = 27 ft³. So, we have the volume equation ...

  V = (1/4)A = 27

  πx(88+x)/4 = 27

  x^2 +88x = 108/π . . . . . multiply by 4/π

  x^2 +88x + 44^2 = 108/π +44^2 . . . . complete the square

  (x +44)^2 = (108/π) +1936 . . . . . . . . . .write the equation as a square

We want the solution that is near zero, so, taking the positive square root, we get ...

  x = -44 +√(108/π +1936) ≈ 0.388934 . . . . feet

The width in inches is 12 times this value, or about 4.667 inches.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05