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Reptile [31]
2 years ago
5

A clothing manufacturer is making scarves that require 3/4 yard for material each. How many can be made from 19 yards of materia

l?
Mathematics
1 answer:
Yanka [14]2 years ago
6 0

Answer:

25

Step-by-step explanation:

1 scarve = 3/4 yards

x = 19 yards

using proportion

x = (19*1)/ 3/4

x = 19*4/3

= 76/3

approximately 25

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Applying our power rule gets us our first derivative,

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\rm 0=2x^{-2/3}+4x^{1/3}

We can apply more factoring.
I hope this next step isn't too confusing.
We want to factor out the smallest power of x from both terms,
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0=2x^{-2/3}\left(1+2x\right)

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Apply your First Derivative Test to further classify these points. You should end up finding that x=-1/2 is an relative extreme value, while x=0 is not.

Let's come back to this,

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\rm f''(x)=-\frac43x^{-5/3}+\frac43x^{-2/3}

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Again, pulling out the smaller power of x, and fractional part,

\rm 0=-\frac43x^{-5/3}\left(1-x\right)

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Applying your Second Derivative Test should verify that both points are in fact inflection points, locations where the function changes concavity.
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\huge\fbox{Answer ☘}

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