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marshall27 [118]
3 years ago
8

Julie tries to keep a very consistent sleep schedule.

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0

Answer:

10 1/2 hours all together but 3 1/2 each day of half sleep

Step-by-step explanation:

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How cos π/3=1/2?<br>having some problems learning continuity.
Bingel [31]

You can show that \cos\frac\pi3=\frac12 by constructing a triangle.

Take two points, O(0, 0) and A(1, 0), and let B be the point on the unit circle such that the angle between the line segments OA and OB is \frac\pi3 radians.

Since both A and B lie on the circle, the line segments OA and OB both have length 1 (same as the circle's radius). We finish constructing the triangle by connect A and B.

Since OB and OA have the same length, triangle OAB is isosceles, but more than that, it's also equilateral. Why? Because the interior angles of any triangle always add to \pi radians. We know one of the angles is \frac\pi3 radians, which leaves a contribution of \frac{2\pi}3 radians between the remaining angles A and B. Angles A and B must be congruent (because OAB is isosceles), which means they also have measure \frac\pi3 radians.

Next, draw an altitude of the triangle through point B, and label the point where it meets the "base" OA, C. Since OAB is equilateral, the altitude BC is also a perpendicular bisector. That means OC has length \frac12, and by definition of \cos we have

\cos\dfrac\pi3=\dfrac{OC}{OB}=\dfrac{\frac12}1=\dfrac12

3 0
3 years ago
Help Fast Please!!!!!!!!! How can you tell if three positive numbers form a Pythagorean triple?
Fiesta28 [93]

Answer/Step-by-step explanation:

Square all three numbers. If the largest number squared is equal to the sum of the squares of the other two, then the numbers form a Pythagorean triple.

<u><em>or</em></u>

Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25

<u><em>either one works</em></u>

3 0
3 years ago
5 times 7/8 then converted to simplest form?
pantera1 [17]
5*7/8 = 4 3/8
5/1 * 7/8 = 35/8
convert into mixed number because numerator is bigger than the denominator so it it
4 3/8
7 0
3 years ago
On Monday Greg walks the entire length of a trail that is 3 1/2 miles long on Tuesday he walks the entire length of a trail that
-Dominant- [34]

Answer:

Step-by-step explanation:

3.5+4.6+2.5 = 10.6

7 0
3 years ago
Read 2 more answers
Using multiplication property of equality solve x/2=6
weeeeeb [17]
\frac{x}{2} = 6
\frac{x}{2} (2) = 6(2)
x=12
5 0
3 years ago
Read 2 more answers
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