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Sindrei [870]
2 years ago
4

A circular pond of radius 6m is surrounded by a path of width 1m.

Mathematics
1 answer:
Novay_Z [31]2 years ago
4 0
Area of pond=pi X 6×6
Area of pond=113.1 square metres
Area of pond and path combined=pi X 7×7
Area combined=153.9 square metres
Area of path=area of both=area of pond=40.8square metres.
Six bags are needed
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Prescription for Marilyn Jones
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Polygon CCC has an area of 404040 square units. Kennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 2 1
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Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the
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Answer:

  • See the graph attached
  • x₁ ≈ - 2.1
  • x₂ ≈ 0.2

Explanation:

To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:

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  • Equatin2:    y = - 1 - x

1) To graph the equation 1 you can use these features of logarithmfunctions:

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  • Range: all real numbers (- ∞ , ∞)

  • x-intercept:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054

  • y-intercept:

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

  • Pick some other values and build a table:

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

  • You can see such graph on the picture attached: it is the red curve.

2) Graphing the equation 2 is easier because it is a line: y = - 1 - x

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3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:

  • <u><em>x₁ ≈ - 2.1</em></u>
  • <u><em>x₂ ≈ 0.2</em></u>

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