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Katarina [22]
3 years ago
12

An electrician is hired to install outdoor lighting. The electrician claims that the relationship between the number of hours wo

rked and the total work fee is porportional. The fee for 5 hours of work is $255
Mathematics
1 answer:
Bingel [31]3 years ago
6 0
<h2>Explanation:</h2><h2></h2>

If we have two variables and can write a relationship between them as:

y=kx \\ \\ \\ Where: \\ \\ \text{k is the constant of proportionality}

Then we say that y varies directly as x or y is directly proportional to x

In this case, let's say:

x:\text{The number of hours worked} \\ \\ y:\text{Total work fee}

Then since we know that the fee for 5 hours of work is $255, then the constant of proportionality is:

k=\frac{255}{5} \\ \\ k=51

Therefore, our model can be written as:

\boxed{y=51x}

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I suppose the integral is

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The integration region corresponds to a sector of a cirlce with radius 5 subtended by a central angle of π/4 rad. We can capture this region in polar coordinates by the set

R=\left\{(r,\theta)\mid0\le r\le5,0\le\theta\le\dfrac\pi4\right\}

Then x=r\cos\theta, y=r\sin\theta, and \mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta. So the integral becomes

\displaystyle\iint_Rxy\,\mathrm dx\,\mathrm dy=\int_0^{\pi/4}\int_0^5r^3\sin\theta\cos\theta\,\mathrm dr\,\mathrm d\theta=\frac{625}{16}

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3 years ago
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x = - 10

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Method A

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Method B:

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As we are dealing with absolute values, the order is not relevant after all, the result remains the same. Take a look:

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