Answer:
sinB= 3/5, tanA=4/3, cosB=4/5
Step-by-step explanation:
Hope I’m not as late but the cost per topping is 80 cents.
By the chain rule,

which follows from
.
is then a function of
; denote this function by
. Then by the product rule,
![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}](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%20dt%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%2B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20df%7D%7B%5Cmathrm%20dx%7D)
and by the chain rule,

so that

Then the ODE in terms of
is

The characteristic equation

has two roots at
and
, so the characteristic solution is

Solving in terms of
gives

Step-by-step explanation:
cos θ - sin θ = √2 sin θ
cos θ + sin θ = √2 sin θ + 2sin θ
cos θ + sin θ = √2(sin θ + √2sin θ)
cos θ + sin θ = √2 cos θ. (Proven)