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Triss [41]
3 years ago
8

You can work a total of no more than 35 hours each week at your two jobs. Housecleaning pays $7 per hour and your sales job pays

$9 per hour. You need to earn at least $314 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.​
Mathematics
1 answer:
Alex787 [66]3 years ago
5 0

Answer: 7x + 9y >_ (more or equal) 314

X + Y <_ ( less or equal) 35

Step-by-step explanation:

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3 years ago
How do you do this question?
ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

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y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

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