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zhannawk [14.2K]
3 years ago
12

Isaac takes a 216-mile trip from

Mathematics
1 answer:
daser333 [38]3 years ago
8 0

Answers:

  • First Blank = 54
  • Second Blank = 162

=============================================

Explanation:

The first blank represents the distance that corresponds to t = 1 hour.

We'll replace t with 1 to get...

d = 54t

d = 54*1

d = 54

Therefore, 54 goes in the first blank. It means that Isaac traveled 54 miles after 1 hour.

------------------

We repeat these steps for t = 3

d = 54*t

d = 54*3

d = 162

This means he traveled 162 miles after 3 hours

So 162 goes in the second blank

-------------------

Side note: your teacher wrote 180 but s/he should have written 108 instead because 54*2 = 108

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irina [24]

Answer:

x-coordinates of relative extrema = \frac{-1}{2}

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Step-by-step explanation:

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Differentiate with respect to x

f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}

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f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1

At x = \frac{-1}{2},

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We know that if f''(a)>0 then x = a is a point of minima.

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So, x-coordinates of the inflexion points are 0, 1

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