# The area a painter can paint varies directly with the amount of time he works. One morning, he paints 204 #ft^2# between 8 a.m. and 12:15 a.m. How do you write a direct variation equation to describe the area #y# covered in #x# hours?

Equation is

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The direct variation equation to describe the area y covered in x hours is:

y = kx

Where y is the area covered, x is the time in hours, and k is the constant of variation. To find k, we can use the given information that the painter painted 204 ft^2 between 8 a.m. and 12:15 p.m., which is a total of 4 hours and 15 minutes, or 4.25 hours. So, substituting the values into the equation:

204 = k * 4.25

Solve for k:

k = 204 / 4.25

k ≈ 48

Therefore, the direct variation equation is:

y = 48x

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To write a direct variation equation to describe the area ( y ) covered in ( x ) hours, we can use the given information to establish the constant of variation ( k ).

First, we need to find the number of hours the painter works. The time between 8 a.m. and 12:15 p.m. is 4 hours and 15 minutes, which can be converted to ( 4.25 ) hours.

Then, we set up the equation using the direct variation formula: ( y = kx ), where ( y ) is the area covered and ( x ) is the number of hours worked.

Now, we can plug in the values we have: ( 204 = k \times 4.25 ).

To solve for ( k ), divide both sides by ( 4.25 ):

[ k = \frac{204}{4.25} ]

[ k \approx 48 ]

So, the direct variation equation to describe the area covered ( y ) in ( x ) hours is:

[ y = 48x ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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