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3 years ago

Find four fractions between 1/10 and 1/8

Mathematics

1 answer:

Alex17521 [72]3 years ago

6 0

9514 1404 393

Answer:

5/48, 5/46, 5/44, 5/42

Step-by-step explanation:

We can choose unit fractions with denominators between 8 and 10, separated by (10-8)/5 = 0.4 units:

1/8.4 = 5/42

1/8.8 = 5/44

1/9.2 = 5/46

1/9.6 = 5/48

Check

1/8 = 0.125
5/42 ≈ 0.119
5/44 ≈ 0.114
5/46 ≈ 0.109
5/48 ≈ 0.104
1/10 = 0.100

_____

Additional comment

There are an infinite number of such fractions. We are given unit fractions with different denominators, so it works reasonably well to choose denominators between those given. Then the trick is to convert the fraction to a ratio of integers. In this case, multiplying by (5/5) does the trick.

Another approach is to write the fractions with a common denominator, then choose numerators between the ones given. For example, 1/10 = 4/40, and 1/8 = 5/40, so you could write some fractions with numerators between 4 and 5. Possibilities are 4.1/40 = 41/400, 4.3/40 = 43/400, 4.7/40 = 47/400, 4.9/40 = 49/400.

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Let's check each case to determine the solution to the problem.

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If the price is marked down by $10$ percent

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case B) If the price is marked down by $25$ percent, the new price will be $\$21$

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If the price is marked down by $35$ percent

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$35\%= \frac{35}{100} =0.35$

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$\$18.20=\$18.20$

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The statement case D) is True

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If the price is marked down by $40$ percent

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$40\%= \frac{40}{100} =0.40$

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maxonik [38]

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$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

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$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

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(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

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Answer:

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B) DNE

Step-by-step explanation:

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you replace t1 from the first equation in the second equation:

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