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sveta [45]
3 years ago
10

Solve the differential equation

d="TexFormula1" title=" \frac{dy}{dx} = 2cos^{2} y" alt=" \frac{dy}{dx} = 2cos^{2} y" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
avanturin [10]3 years ago
5 0

tany =2x+C is the required differential equation.

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Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen we
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<u>Answer-</u>

Set of constraints to model the problem are,

12x+9y\geq 510

y \leq 2x

y \geq 25

<u>Solution-</u>

<em>x = the number of lawns weeded by Gwen,</em>

<em>y = the number of dogs walked by Fabio.</em>

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

\text{Earnings of Gwen} = 12x

\text{Earnings of Fabio} = 9y

\text{Total earning} = 12x+9y

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

12x+9y\geq 510

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

y \leq 2x

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

y \geq 25



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