300.84m^2
First, set up the equation
A=27.6•10.9
Next, multiply(use a calculator)
And you get the answer.
^2 means squared.
ABC and HJK are congruent and the corresponding sides and angles are equal. Side HJ is congruent with side AB so HJ is also 3.5cm in length.
Let
be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are
![\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Ds_A%28t%29%20%3D%20vt%5C%5Cs_B%28t%29%20%3D%20-%5Cdfrac%7B8%7D%7B7%7Dvt%2B450%5Cend%7Bcases%7D)
where
are the positions of trains A and B respectively, and t is the time in hours.
The two trains meet if and only if
, and we know that this happens after two hours, i.e. at ![t=2](https://tex.z-dn.net/?f=t%3D2)
![\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Ds_A%282%29%20%3D%202v%5C%5Cs_B%282%29%20%3D%20-%5Cdfrac%7B16%7D%7B7%7Dv%2B450%5Cend%7Bcases%7D%5Cimplies%202v%20%3D%20-%5Cdfrac%7B16%7D%7B7%7Dv%2B450)
Solving this equation for v we have
![2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105](https://tex.z-dn.net/?f=2v%20%3D%20-%5Cdfrac%7B16%7D%7B7%7Dv%2B450%20%5Ciff%20%5Cdfrac%7B30%7D%7B7%7Dv%3D450%20%5Ciff%20v%3D%5Cdfrac%7B450%5Ccdot%207%7D%7B30%7D%20%3D%20105)
So, train A is travelling at 105 km/h. This implies that train B travels at
![105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}](https://tex.z-dn.net/?f=105%5Ccdot%20%5Cdfrac%7B8%7D%7B7%7D%20%3D%2015%5Ccdot%208%3D120%20%5Ctext%7B%20km%2Fh%7D)
X=2 so 2+4=6 so y=6. I just gone ovee this unit aswell.
This is just here for the 20 character limit but the answer is in the picture.