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Anna35 [415]
3 years ago
15

Carol is going to buy a purse she found. It is originally $120.00, but has been marked down 25%. When carol goes to buy the purs

e she has to pay 8% tax on the discounted price. What is the final cost of the purse?
Mathematics
1 answer:
german3 years ago
5 0
$97.2


120*.75 =90 (discounted price)
90*.08 = 7.2 (amount sales tax)

90 + 7.2= 97.2
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Answer:

The homogeneous differential equation is

d^4y/dx^4 + 37d²y/dx² + 36 = 0

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Step-by-step explanation:

We want to find a homogeneous linear differential equation with constant coefficients whose general solution is given as

y = c1 cos(x) + c2 sin(x) + c3 cos(6x) + c4 sin(6x)

This, we are working in reverse. Instead of having a differential equation, and writing and solving it's characteristic equation, before writing it's general solution, we are already given the general solution, so, we work in reverse.

Given

y = c1 cos(x) + c2 sin(x) + c3 cos(6x) + c4 sin(6x)

By observation, we have

(1) Homogeneous differential equation of the fourth order, because of the number of constants

(2) Two pairs of complex roots, that's why we have cosines, and sines.

Knowing that if

m = a ± ib

The general solution is

y = (e^ax)(c1 cos bx + c2 sin bx)

We can now write for

y = [c1 cos(x) + c2 sin(x)] + [c3 cos(6x) + c4 sin(6x)]

As

m = 0 ± i

and

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So that we have

m = √(-1)

m = √(-36)

m² = -1

m² = -36

m² + 1 = 0

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The auxiliary equation is therefore

(m² + 1)(m² + 36) = 0

m^4 + 36m² + m² + 36 = 0

m^4 + 37m² + 36 = 0

Finally, the homogeneous differential equation is

d^4y/dx^4 + 37d²y/dx² + 36 = 0

Or

y^(iv) + 37y'' + 36 = 0

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