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Simora [160]
3 years ago
10

Evelyn has 12.7 quarte of fruit punch in a cooler. She pours the fruit punch into glasses. She fills 5 glasses, each with a capa

city of 0.36 quart. Then she fills 8 glasses, each with a capacity of 0.52 quart. How much fruit punch is left in the cooler?
Mathematics
1 answer:
Alexus [3.1K]3 years ago
7 0
There is 6.74 quarts left in the cooler.

Since 5 of the glasses have a capacity of 0.36 qt, this is a total of 5(0.36) = 1.8 qt.  The 8 glasses that have a capacity of 0.52 qt have a total of 8(0.52) = 4.16 qt.  This gives a total of 4.16+1.8 = 5.96 qt.

To find the remaining, subtract from 12.7:
12.7-5.96 = 6.74 qt.
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Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

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We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = \int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx

= \sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}

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= 6 - 1.5

= 4.5 sq. units. (Answer)

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