A. A bicycle shop marks down each bicycle's selling price b by 22% for a holiday sale.
1 answer:
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Given a solution 
, we can attempt to find a solution of the form 
. We have derivatives
Substituting into the ODE, we get
Setting
, we end up with the linear ODE
Multiplying both sides by
, we have
and noting that
![\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5Bx%28%5Cln%20x%29%5E2%5Cright%5D%3D%28%5Cln%20x%29%5E2%2B%5Cdfrac%7B2x%5Cln%20x%7Dx%3D%28%5Cln%20x%29%5E2%2B2%5Cln%20x)
we can write the ODE as
![\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5Bwx%28%5Cln%20x%29%5E2%5Cright%5D%3D0)
Integrating both sides with respect to
, we get
Now solve for
:
So you have
and given that
, the second term in 
is already taken into account in the solution set, which means that 
, i.e. any constant solution is in the solution set.
Substituting into the ODE, we get
Setting
Multiplying both sides by
and noting that
we can write the ODE as
Integrating both sides with respect to
Now solve for
So you have
and given that
Answer: The answer is (C) (4,1).
Step-by-step explanation: Given points are A(0,3), B(-1,4) and C(2,-1). Obviously, these points will form a triangle. We need to find the co-ordinates of the point B', which is formed after rotating the figure counter-clockwise 90 degrees.
The point B(-1,4) lies in the second quadrant. After rotating 90 degrees counter-clockwise, the this point will lie in the first quadrant. So, both the x-coordinate and y-coordinate will be positive. Also, the two coordinates will exchange. Please see the attached figure.
Thus, the coordinates of point B' are (4,1).
Hence, (C) is the correct option.
