Answer:
3
Step-by-step explanation:
3 is the complete oposite of -1/3 in terms of slopes, therefore they are perpendicular to each other.
Step-by-step explanation:

The complete factorisation of 50a²b⁵ − 35a⁴b³ + 5a³b⁴ is 5a²b³(10b² - 7a² + ab)
<h3>How to factorise?</h3>
Factorisation is the process of writing an expression as a product of two or more common factors.
The expression is written as a product of several factor.
Therefore,
50a²b⁵ − 35a⁴b³ + 5a³b⁴
Hence, the complete factorisation is as follows;
5a²b³(10b² - 7a² + ab)
learn more on factorisation here: brainly.com/question/2272501
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Answer:

Step-by-step explanation:
![\dfrac 12 \left[\sin(a+b)+\sin(a-b) \right]\\\\\\=\dfrac 12\left[ 2 \sin a \cos b\right]\\\\\\=\sin a \cos b](https://tex.z-dn.net/?f=%5Cdfrac%2012%20%5Cleft%5B%5Csin%28a%2Bb%29%2B%5Csin%28a-b%29%20%5Cright%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%2012%5Cleft%5B%202%20%5Csin%20a%20%5Ccos%20b%5Cright%5D%5C%5C%5C%5C%5C%5C%3D%5Csin%20a%20%5Ccos%20b)