Hi,
could I please have some help with chapter 10 Exercise 10.07 questions.
Thank you
Edit: Jake beat me but I'll post anyway because our answers end up different, mistake in finding your constant Jake? I'm doing mentally so not sure Hi there! My working might differ slightly from the typical method you use in General Math, but it should be close! There is also an error in the wording of the question, it should read,
of the cable is varied.
So, what we have here is a proportional relationship, because \(M\) grows in proportion to \(t^2\).
We can write this in two ways:
Here, \(k\) is our
constant of proportionality. We can use either of these relationships to proceed (they are, in effect, the same thing) but I'll use the second one.
So we know that when \(t=1.2\), \(M=1440\). This lets us find \(k\):
What this proves is that the weight that the cable can carry is always
one thousand times greater than the square of the thickness of the cable. We can use this to solve both our questions. For Question A, if we have a thickness of 0.7 centimetres:
Try your luck at Question B by substituting into the equation, the only difference being you'll have to rearrange, because you are looking for t!
You don't have to use the equation btw, you can just figure out the relationship between \(M\) and \(t^2\) and then apply it, but the equation formalises the matter