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3 years ago

15

Vincent started the year with $231 in his account at the health spa. Each time he uses the spa, $6 is taken out of the account.

How many more times can he use the spa if he has already had $48 taken out of his account this year?

1 answer:

SpyIntel [72]3 years ago

6 0

Answer:

Vincent would have 30.5 more visits, but since you can't have half a visit technically speaking, round up to 31 if it is allowed.

Step-by-step explanation:

$231 - $48 = $183

$183 divided by $6 = 30.5

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a) The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ .

b) The integrating factor for the <em>ordinary</em> differential equation is $-\frac{1}{x}$ .

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a) In this case we need to separate each variable ( $y, t$ ) in each side of the identity:

$6\cdot \frac{dy}{dt} = y^{4}\cdot \sin^{4} t$ (1)

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The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ . $\blacksquare$

b) In this case we need to solve a first order ordinary differential equation of the following form:

$\frac{dy}{dx} + p(x) \cdot y = q(x)$ (2)

Where:

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$q(x)$ - Particular function

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$\frac{dy}{dx} -\frac{1}{x}\cdot y = x^{2}+\frac{1}{x}$ (3)

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The solution for (2) is presented below:

$y = e^{-\int {p(x)} \, dx }\cdot \int {e^{\int {p(x)} \, dx }}\cdot q(x) \, dx + C$ (4)

Where $C$ is the integration constant.

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$y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$

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