Triangle ABC is similar to triangle LMN
m<A = m<L = 60
m<C = m<N
m<B = m<M
Lets x = m<M
so
m<C = m<N = 3x
and sum of interior angles of a triangle = 180
so
m<L + m<N + m<M = 180
60 + 3x + x + 180
4x + 60 = 180
4x = 120
x = 30
m<M = x = 30
answer
m<M = 30°
Answer:
![\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bd%28y%28t%29%29%7D%7Bdt%7D%20%3D%5Cdisplaystyle%5Cfrac%7Bd%28f%28u%28t%29%29%29%7D%7Bdt%7D%20%3D%20f%27%28u%28t%29%29.u%27%28t%29)
Step-by-step explanation:
The chain rule helps us to differentiate functions and a composition of two functions.
Let r(u) and s(u) be two function. Then, composition of these two functions can be be differentiated with the help of chain rule. It states that:
![\displaystyle\frac{d(r(s(u)))}{du} = r'(g(u)).s'(u)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bd%28r%28s%28u%29%29%29%7D%7Bdu%7D%20%3D%20r%27%28g%28u%29%29.s%27%28u%29)
Now, we are given
![y(t) = f(u(t))](https://tex.z-dn.net/?f=y%28t%29%20%3D%20f%28u%28t%29%29)
Then, by chain rule, we have:
![\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bd%28y%28t%29%29%7D%7Bdt%7D%20%3D%5Cdisplaystyle%5Cfrac%7Bd%28f%28u%28t%29%29%29%7D%7Bdt%7D%20%3D%20f%27%28u%28t%29%29.u%27%28t%29)
Answer to 2/3 + 1/6 is 5/6.
Answer:
![x=6](https://tex.z-dn.net/?f=x%3D6)
Step-by-step explanation:
5x - 24 = 3 * 2
5x - 24 = 6
5x = 30
x = 6