Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Electronics

The resistance y (in ohms) of 1000 feet
of solid copper wire at 68 degrees Fahrenheit is
y = (10,370)/(x^2) where x is the diameter of the wire in mils (0.001 inch).

(a) Complete a table given the following x-values:.

x: 5 10 20 30 40 50, 60, 70, 80, 90, 100
y:

(b) Use the table of values in part (a) to sketch a graph
of the model. Then use your graph to estimate the
resistance when x = 85.5.

(c) Use the model to confirm algebraically the estimate
you found in part (b).

(d) What can you conclude about the relationship
between the diameter of the copper wire and the
resistance?

For part (a), I must evaluate for y given all the values of x.

For part (b), I must graph the points formed by the values
of x and y. How do I use the graph to estimate the resistance when x is
85.5, a value for x not given in the table?

For part (c), I need this to be explained. How do I estimate what is found
in part (a)?

I don't understand part (d).

Thanks

Last edited by mathland (2021-05-05 19:56:24)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Electronics

For part (a), I must evaluate for y given all the values of x.  Yes.

For part (b), I must graph the points formed by the values
if and y. How do I use the graph to estimate the resistance when x is
85.5, a value for x not given in the table?

It's called 'interpolation'.  Literally 'between the points'. Once you have the points plotted you'll see they lie on a curve.  If you try to connect them with a smooth curve, you can then read off the y value for x = 85.5

The formula will give you the actual y value.  It should be about the same as your estimate using interpolation.

(d) I'm not sure either.  If the formula was x^2 we would say it's a square law.  As it's 1/x^2 I guess they want you to say it's an inverse square law.  That's like Newton's law for gravity.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Electronics

For part (a), I must evaluate for y given all the values of x.  Yes.

For part (b), I must graph the points formed by the values
if and y. How do I use the graph to estimate the resistance when x is
85.5, a value for x not given in the table?

It's called 'interpolation'.  Literally 'between the points'. Once you have the points plotted you'll see they lie on a curve.  If you try to connect them with a smooth curve, you can then read off the y value for x = 85.5

The formula will give you the actual y value.  It should be about the same as your estimate using interpolation.

(d) I'm not sure either.  If the formula was x^2 we would say it's a square law.  As it's 1/x^2 I guess they want you to say it's an inverse square law.  That's like Newton's law for gravity.

Bob

There is no answer for this problem in the back of the book. So, part (d) remains a mystery.