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larisa86 [58]
3 years ago
15

Melissa needs to buy some pencils. Brand A has a pack of 24 penals for $8.77. Brand B has a pack of 26 pencils for $9.54

Mathematics
1 answer:
almond37 [142]3 years ago
3 0

Answer:

Brand A is the better buy.

Step-by-step explanation:

You can use proportions to set up and solve this problem.

24 1

----- = ------

8.77 $.365 is the unit price for Brand A

26 1

----- = ----

9.54 $.366 is the unit price for Brand B

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I suppose you mean

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Differentiate one term at a time.

Rewrite the first term as

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Then the product rule says

\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'

Then with the power and chain rules,

\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}

Simplify this a bit by factoring out \frac12 (36-x^2)^{-3/2} :

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Then by the chain rule,

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