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scoundrel [369]
3 years ago
9

Martina has a circle with a diameter

Mathematics
1 answer:
klasskru [66]3 years ago
4 0

Answer:

The ratio of the circumference to its diameter remains the same.

Step-by-step explanation:

Given,

diameter of circle = 6 inch

diameter is doubled.

New diameter of circle = 2 x 6 = 12 inch

We know that,

The Circumference of a circle is 2 π r or π d where r is the radius of the circle and d is the diameter of the circle.

Circumference of the circle when the diameter is 6 inches.

C₁ =   6π

Ratio of circumference to diameter

Ratio = \dfrac{6\pi}{6}

Ratio =  π

When the diameter is 12 inches

C₂ = 12 π

Ratio of circumference to diameter

Ratio = \dfrac{12\pi}{12}

Ratio =  π

Now, the correct statement is the ratio of the circumference to its diameter remains the same if the diameter is doubled.

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The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)

Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1

We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
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Now we know the equation is
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_____
If we like, we can expand it to
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=========
An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
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Then the equation of the graph can be written as
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