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hodyreva [135]
3 years ago
13

In right triangle ABC, sin M = cos 61. If 0

Mathematics
1 answer:
Eva8 [605]3 years ago
8 0

Note: Consider we need to find the value of M if 0^\circ

Given:

In a right triangle ABC,

\sin M=\cos 61^\circ

To find:

The value of M.

Solution:

We have,

\sin M=\cos 61^\circ

It can be rewritten as:

\sin M=\cos (90^\circ-29)^\circ

\sin M=\sin 29^\circ                   [\because \sin (90^\circ-\theta)=\sin \theta]

On comparing both sides, we get

M=29^\circ

Therefore, the value of M is 29 degrees.

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Geometric sequences HELP ASAP!
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Given:

The table for a geometric sequence.

To find:

The formula for the given sequence and the 10th term of the sequence.

Solution:

In the given geometric sequence, the first term is 1120 and the common ratio is:

r=\dfrac{a_2}{a_1}

r=\dfrac{560}{1120}

r=0.5

The nth term of a geometric sequence is:

a_n=ar^{n-1}

Where a is the first term and r is the common ratio.

Putting a=1120, r=0.5, we get

a_n=1120(0.5)^{n-1}

Therefore, the required formula for the given sequence is a_n=1120(0.5)^{n-1}.

We need to find the 10th term of the given sequence. So, substituting n=10 in the above formula.

a_{10}=1120(0.5)^{10-1}

a_{10}=1120(0.5)^{9}

a_{10}=1120(0.001953125)

a_{10}=2.1875

Therefore, the 10th term of the given sequence is 2.1875.

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