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
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<em>Check</em>
- 1/8 = 0.125
- 5/42 ≈ 0.119
- 5/44 ≈ 0.114
- 5/46 ≈ 0.109
- 5/48 ≈ 0.104
- 1/10 = 0.100
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<em>Additional comment</em>
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.
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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.
Using trigonometric relations, we will see that:
sin(θ ) = -0.8
<h3>
How to get the sine of the angle?</h3>
For any point (x, y), the angle between the positive x-axis and the ray that connects the origin with the point (x, y) is:
θ = Atan(y/x)
In this case, the point is (3, -4), then the angle is:
θ = Atan(-4/3) = -53.13°
Then the sine of theta is:
sin(θ = -53.13°) = -0.8
If you want to learn more about trigonometric functions:
brainly.com/question/8120556
#SPJ1
Discount = 35/100 * 40 = $14
Price = $40- $14 = $26
Cylinder's volume = 1330.5 cm^3
Step-by-step explanation:
radius, r = diameter, d / 2
= 11/2
= 5.5 cm
Volume = π r^2 h
= π × 5.5^2 × 14
= 423.5π
= 1330.5 cm^3
