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const2013 [10]
4 years ago
8

What are two decimals between 0.3 and 0.5?

Mathematics
1 answer:
konstantin123 [22]4 years ago
3 0
0.4 and 0.45


 look for two that are in the middle of 0.3 and 0.5
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Find sin(2x), cos(2x), and tan(2x) from the given information.
larisa86 [58]

Since \cot(x)=\frac{2}{3} and \cot^{2} x+1=\csc^{2} x, we know that:

\left(\frac{2}{3} \right)^{2}+1=\csc^{2} x\\\\\frac{13}{9}=\csc^{2} x\\\\\csc x=\frac{\sqrt{13}}{3}

If \csc x=\frac{\sqrt{13}}{3}, this means that \sin x=\frac{3}{\sqrt{13}} and by the Pythagorean identity,

\sin^{2} x+\cos^{2} x=1\\\left(\frac{3}{\sqrt{13}} \right)^{2}+\cos^{2} x=1\\\frac{9}{13}+\cos^{2} x=1\\\cos^{2} x=\frac{4}13}\\\cos x=\frac{2}{\sqrt{13}}

  • Using the double angle formula for sine, \sin(2x)=2\left(\frac{3}{\sqrt{13}} \right)\left(\frac{2}{\sqrt{13}} \right)=\boxed{\frac{12}{13}}
  • Using the double angle formula for cosine, \cos(2x)=1-2\left(\frac{3}{\sqrt{13}} \right)^{2}=\boxed{-\frac{5}{13}}
  • So, since tan=sin/cos, \tan (2x)=\frac{\sin(2x)}{\cos(2x)}=\frac{\frac{12}{13}}{-\frac{5}{13}}=\boxed{-\frac{12}{5}}

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2 years ago
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3. A regular hexagon has six equilateral triangles with a common
hichkok12 [17]

Answer:

if the height of the triangle is 8 in, its side is 9.2379, and this side is also the side of the hexagon, so the perimeter is 6*9.2379 = 55.43 in

Step-by-step explanation:

As the hexagon is regular, each of those triangles will also be regular.

So if the height of one triangle is 8 inches, we can find the side of the triangle with the height formula of a regular triangle:

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8 = side * 0.866

side = 8/0.866 = 9.2379

The side of the triangle will also be the side of the hexagon. So the perimeter of the hexagon will be:

P = 6 * 9.2379 = 55.43 inches

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She receives 21. 1/5 of 30 is 6, or the number of picture messages Lilly receives. 7/8 of 24, the number of remaining messages, is equal to 21.
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