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tresset_1 [31]
3 years ago
15

Morgan is making two cookie recipes. Recipe A calls for one-third less than twice the number of cups of sugar that Recipe B call

s for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?
Mathematics
1 answer:
horsena [70]3 years ago
7 0

Answer:

1 & 1/6

Step-by-step explanation:

You only need half the amount of sugar so you multiply by 1/2. so 2 cups and 1/3.

2\1 X 1/2 = 2/2=1 cup

1/3X1/2=1/6

1+1/6= 1 & 1/6

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An open box is to be constructed so that the length of the base is 3 times larger than the width of the base. If the cost to con
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Step-by-step explanation:

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L = 3w --- (1)volume = l \times w \times h \\ \\ 88 =  (3w)   \times w  \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\

The construction cost now is:

C = 4(l \times w) + 2 ( w  \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w  \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}

Now, to determine the minimum cost:

\dfrac{dC}{dw}= 0  \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}

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Now;

length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet

height = ( 88})^{1/3} (3)^{1/3} \ feet

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