Given:
Total solution : 1000mL
Pure acetic acid = 26mL
To find:
The percent concentration of given solution.
Solution:
We know that,
Putting the given values, we get
Therefore, the percent concentration of this solution is 2.6%.
Substitute
, so that
![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%2B%5Cdfrac1x%5Cleft%28%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D%5Cright%29%3D%5Cdfrac1%7Bx%5E2%7D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D-%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%29)
Then the ODE becomes
which has the characteristic equation
with roots at
. This means the characteristic solution for
is
and in terms of
, this is
From the given initial conditions, we find
so the particular solution to the IVP is
Answer:
b 375
Step-by-step explanation:
Answer: 78
Step-by-step explanation:
First, we want to find the area of the outer triangles. Remember that the equation to finding the area of a triangle is (l x h) x 1/2. So, let’s substitute the values into the equation. It’ll be (6 x 7) x 1/2. Let’s solve! 6 x 7 = 42. Then, 42 x 1/2 = 21. But let’s not forget that we only found the area of one triangle. We still need to find the area of the other outer triangles. So, to do this, we take 21 and multiply by 3 since the other outer triangles have the same dimensions. We would get 63 as our total area for the outer triangles.
Next, we need to find the area for the inner triangle. We will use the same equation: (l x h) x 1/2. Let’s substitute! (6 x 5) x 1/2 will be our final equation. Now, let’s solve. 6 x 5 = 30. 30 x 1/2 = 15. So, as a process of elimination, our area for the inner triangle is 15.
Finally, we need to add the total areas we found together. Our total areas were 63 and 15. Let’s put this into an equation: 63 + 15 = ?. So, 63 + 15 = 78. So, after a long process, 15 is our answer!
Hope this helped!
