The variable 𝑝 is inversely
proportional to the square of the variable 𝑞. Circle the correct equation given
that 𝑘 is a constant. The options are 𝑝 equals 𝑘 over
𝑞, 𝑝 equals 𝑘 over 𝑞 squared, 𝑝 equals 𝑘𝑞, and 𝑝 equals 𝑘𝑞 squared.
So what I’m gonna do is look at
each of our possible answers in turn. The first one is 𝑝 equals 𝑘 over
𝑞. So 𝑝 equals 𝑘 over 𝑞 can also be
written as 𝑝 and then the proportionality sign then one over 𝑞. And what this means is that 𝑝 is
inversely proportional to 𝑞.
Well, if we look at the question,
we want the variable 𝑝 to be inversely proportional to 𝑞. So that part is correct. However, we want it to be inversely
proportional to the square of the variable 𝑞 and that’s not the case in this first
answer. So therefore, this first answer is
not the correct one.
Well, if we take a look at the
second answer, we’ve got 𝑝 again is inversely proportional. So that’s the first part
correct. And then, it says “to 𝑞 squared”
because we have 𝑞 squared as the denominator. Well, this is correct as well
because we were looking for the variable 𝑝 to be inversely proportional to the
square of the variable 𝑞. So therefore, this looks like it’s
gonna be the correct answer. But we’ll double check the last two
just to make sure.
Well, we can deal with the last two
together. Because if we look at them both, we
have 𝑝 equals 𝑘𝑞 and 𝑝 equals 𝑘𝑞 squared. Well, both of these are not one
over. So they’re not inversely
proportional. They’re both in fact directly
So as we’re looking for an
inversely proportional relationship, we can definitely rule these two out. So therefore, we can say that the
second equation is definitely the correct equation to show that the variable 𝑝 is
inversely proportional to the square of the variable 𝑞.