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2 years ago

What is 3 1\8 as a fraction in simplest form ?

Mathematics

1 answer:

Leno4ka [110]2 years ago

6 0

$3*8=24 \\ \\ \frac{24+1}{8} \\ \\ \frac{25}{8} \\ \\ 3 \frac{1}{8} =\frac{25}{8}$

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Let sin t = a, cos t = b, and tan t = c. Write the expression in terms of a, b, and c.

maks197457 [2]

Answer:

$a+b-c$

*Note c could be written as a/b

Step-by-step explanation:

-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)

The identities I'm about to apply:

$\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)$

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let's apply the difference identities to all three terms:

$-[\sin(-t)\cos(8\pi)+\cos(-t)\sin(8\pi)]+[\cos(-t)\cos(2\pi)+\sin(-t)\sin(2\pi)]+\frac{\tan(-t)-\tan(5\pi)}{1+\tan(-t)\tan(5\pi)}$

We are about to use that cos(even*pi) is 1 and sin(even*pi) is 0 so tan(odd*pi)=0:

$-[\sin(-t)(1)+\cos(-t)(0)]+[\cos(-t)(1)+\sin(-t)(0)]+\frac{\tan(-t)-0}{1+\tan(-t)(0)$

Cleaning up the algebra:

$-[\sin(-t)]+[\cos(-t)]+\frac{\tan(-t)}{1}$

Cleaning up more algebra:

$-\sin(-t)+\cos(-t)+\tan(-t)$

Applying that sine and tangent is odd while cosine is even. That is,

sin(-x)=-sin(x) and tan(-x)=-tan(x) while cos(-x)=cos(x):

$\sin(t)+\cos(t)-\tan(t)$

Making the substitution the problem wanted us to:

$a+b-c$

Just for fun you could have wrote c as a/b too since tangent=sine/cosine.

8 0

3 years ago

How much would you have to

Juliette [100K]

Answer:

If it went up it would be: 50596.35 and if it went down it would be: 7556.66

Step-by-step explanation:

Here will be the function if it went up:

20000(1+0.0475)^20

Here’s if it went down:

20000(1-0.0475)^20

7 0

1 year ago

Water level in a well was 20m below ground level. During rainy season, rainwater collected in different water tanks was drained

IgorC [24]

Answer:

17 m

Step-by-step explanation:

As shown in the figure, $A_0-B_0$ is the ground level, $A_1-B_1$ is the old level of water which was at 20 m below ground level, $A_2-B_2$ is the new level of water which is 5m above of old level. The height of wall of the well, 1.20 m, and the the pelly at 80 cm =0.80 m, has been shown too.