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posledela
3 years ago
8

The intensity of light bulb measured in watts per square meter (w/m^2), varies inversely as the square of the distance d from th

e light bulb. suppose is 45 w/m^2 when the distance is 5 m. find the intensity when the distance from the light bulb is 7 m away
Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Answer:

I(7)   =  22.96 W/m²

Step-by-step explanation:

Let intensity of light, be  I(d)   where d is distance. There must be a proportionality factor K such as

I(d)  = K /d²

Now for d = 5 m    I(d)  =  K* 1/d²

then  45 * 25 = K

K =  1125

To find the intensity when the distance from the light bulb is 7 m away

I(7)   =  K / 49

I(7)   =  1125/49   W/m²

I(7)   =  22.96 W/m²

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\bf ~~~~~~~~~~~~\textit{internal division of a line segment}&#10;\\\\\\&#10;A(-4,-8)\qquad B(11,7)\qquad&#10;\qquad \stackrel{\textit{ratio from A to B}}{3:7}&#10;\\\\\\&#10;\cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(-4,-8)=3(11,7)\\\\[-0.35em]&#10;~\dotfill\\\\&#10;C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]&#10;~\dotfill


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