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3 years ago

How do you do this question?

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

5 0

Step-by-step explanation:

y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1

dy/dx = 12√x

Arc length is:

s = ∫ ds

s = ∫₀¹ √(1 + (dy/dx)²) dx

s = ∫₀¹ √(1 + (12√x)²) dx

s = ∫₀¹ √(1 + 144x) dx

If u = 1 + 144x, then du = 144 dx.

s = 1/144 ∫ √u du

s = 1/144 (⅔ u^(³/₂))

s = 1/216 u^(³/₂)

Substitute back:

s = 1/216 (1 + 144x)^(³/₂)

Evaluate between x=0 and x=1.

s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]

s = 1/216 (145)^(³/₂) − 1/216

s = (145√145 − 1) / 216

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Great tennis players use Hexrackets. There if you use a Hexracket, you are a great tennis nyer.

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Answer:

The conclusion is invalid.

The required diagram is shown below:

Step-by-step explanation:

Consider the provided statement.

Great tennis players use Hexrackets. Therefore, if you use a Hexracket, you are a great tennis player.

From the above statement we can concluded that Great tennis players use Hexrackets. But it may be possible that some people who use a haxracket are not great tennis player.

Therefore, the conclusion is invalid.

The required diagram is shown below:

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