Match each label to the correct location.

Mathematics

1 answer:

Nina [5.8K]4 years ago

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Match each label to the correct location.

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Could anyone help me with this whole question? The bottom drop-down question options are, does or does not

Alina [70]

Answer:Values for the coefficient in the product k:

$a=b=c=d=3*10^8$ , so the first four boxes should be filled with the number "3"

Drop down arrow: "does"

Step-by-step explanation:

We perform all the products of wavelength time frequency indicated for the column of the quantity "k":

$a$ = $1 * 10^{-10} * 3\, * 10^{18} = 3 * 10^{-10+18} = 3 * 10^{8}$ =

$b=1 * 10^{-1}*3*10^9=3* 10^{-1+9}=3*10^8$

$c=600*10^{-6}*5*10^{11}=3000*10^{-6+11}=3000*10^5=3*10^3*10^5=\\=3*10^{3+5}=3*10^8$

$d=4*10^{-7}*7.5*10^{14}=30.0*10^{-7+14}=30*10^7=3*10*10^7=\\=3*10^{1+7}=3*10^8$

Therefore, all products of these different wavelengths and their associated frequencies render the exact same answer : $3*10^8$ , which means that as one of these quantities increase, the other one will decrease in the same proportion to give the same numerical answer.

This means that the two quantities are associated via inverse proportionality. As seen in the equation below, if the quantities "x" and "y" are related by inverse proportionality (shown as one equals a constant "A" divided by the other variable), their product x*y will give that constant value "A" (which in our case is $3*10^8$ .

$x=\frac{A}{y} \\x*y=A$