compare and contrast the difference between simplify a fraction and simplify a radical. What is the ultimate goal for each?
1 answer:
<u>Compare:</u><u>
</u>- The goal of reducing a radical and a fraction is to literally simplify the numbers to make them easier to work with
<u>
Contrast:
</u>- The action of simplifying fractions<u /> is dividing the numerator and denominator by a common factor.
- The action of simplifying radicals is making sure the radicand has no square factors. You separate the radicand into two parts, one of which can be square rooted into a whole number.
<em>Example:</em>
</u>- The goal of reducing a radical and a fraction is to literally simplify the numbers to make them easier to work with
<u>
Contrast:
</u>- The action of simplifying fractions<u /> is dividing the numerator and denominator by a common factor.
- The action of simplifying radicals is making sure the radicand has no square factors. You separate the radicand into two parts, one of which can be square rooted into a whole number.
<em>Example:</em>
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Answer: <em>S</em> ≈ 48.2°
Step-by-step explanation:
We can use trigonometry functions to solve.
Looking at angle <em>S</em>, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.
We can find the height of the altitude by the ratio of sin. See my attachment.
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°