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3 years ago

According to astronomers what is a "light year" math worksheet

Mathematics

1 answer:

lubasha [3.4K]3 years ago

3 0

According to NASA, a light year is approximately 6 trillion miles

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Find the value of tan(sin^-1(1/2))

suter [353]

If you know that $\sin\dfrac\pi3=\dfrac12$ , then you know right away

$\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3$

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Otherwise, you can derive the same result. Let $\theta=\sin^{-1}\dfrac12$ , so that $\sin\theta=\dfrac12$ . $\sin^{-1}$ is bounded, so we know $-\dfrac\pi2\le\theta\le\dfrac\pi2$ . For these values of $\theta$ , we always have $\cos\theta\ge0$ .

So, recalling the Pythagorean theorem, we find

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2$

Then

$\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3$

as expected.

5 0

3 years ago

Read 2 more answers

A reasonable estimate of the

lyudmila [28]

Answer:

Step-by-step explanation:

6 0

3 years ago

A discount bookstore sells hardcover books for $12 and paperback books for $6. The number of hardcover books, x, sold one day wa

Thepotemich [5.8K]

Answer: the system of equations that represents this situation are

12x + 6y = 180

x = 2y

Step-by-step explanation:

Let x represent the number of hardcover books that were sold in a day.

Let y represent the number of paperback books that were sold in a day.

The discount bookstore sells hardcover books for $12 and paperback books for $6. The total sales that day were $180. It means that

12x + 6y = 180

The number of hardcover books sold that day was twice the number of paperback books. It means that

x = 2y

8 0

3 years ago

A cylinder has a diameter of 8 inches and a volume of 1287 cubic inches. What is the height of

fredd [130]

Answer:

25.62

Step-by-step explanation:

the answer is rounded and pi was 3.14 to solve this

8 0

3 years ago

Point B is a point of tangency. Find the radius r of OC.<br> А 9<br> B<br> r<br> n

insens350 [35]

Answer:

Radius, r, is 3.75

Step-by-step explanation:

From the given diagram,

AB = 9

AC = 6 + r

BC = r

Thus applying the Pythagoras theorem, we have;

$/AC/^{2}$ = $/AB/^{2}$ + $/BC/^{2}$

$(6 + r)^{2}$ = $9^{2}$ + $r^{2}$

36 + 12r + $r^{2}$ = 81 + $r^{2}$

collecting like terms,

12r = 81 - 36

12r = 45

r = $\frac{25}{12}$

= 3.75

r = 3.75

The radius is 3.75.

3 0

3 years ago