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Jlenok [28]
2 years ago
10

How much will it cost to pour a circular slab 18 ft in diameter by 3 in. For a patio if the concrete costs $40.00 per cubic yard

? (1 cubic yard = 27 cubic feet)
Mathematics
1 answer:
valkas [14]2 years ago
7 0

Answer:

$94.24

Step-by-step explanation:

Given :

Diameter of circular slab = 18feet

Thickness of slab = 3 inches ; inches to ft = 3 /12 = 0.25 feets

Volume of slab = πd²t/4 = (π*18²*0.25) / 4 = 63.6 ft³

1 cubic yard = 27 feet

Volume in yard = 63.6 / 27 = 2.356 yd³

Concrete = $40 per yd³

Cost = $40 * 2.356 = $94.24

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Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.
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<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with f^{-1}(x)

Given that:

I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = a^{-1}(x) = a(x)  Hence, I is true.

II. y =\dfrac{1}{x}

Replacing y with and x with y:

x =\dfrac{1}{y}

x=\dfrac{1}{a^{-1}(x)}

\Rightarrow a^{-1}(x) = \dfrac{1}{x}

a^{-1}(x) = a(x)  Hence, II is true.

III. y =x^{2}

Replacing y with and x with y:

x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)

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Replacing y with and x with y:

x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)

Hence, IV is not true.

<em>Correct answer:</em>

<em>A. I and II</em>

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