Solving for d in a Simple Math Problem

[CRich]

simple math...just not for me

I'm currently in Mechanics of Materials and I have reduced my problem to something similar to: 510/7.6=8.25/((pi/4)*d^2)

how do I solve for d? I have been given the answer (from the back of the book) but i don't remember how to solve for d...by the way the above numbers are random and not from my text...but it is similar...thx crich

 

[Pinu7]

There are a couple possible first-steps to take.

1. Take the reciprocal of both sides.

2. Multiply both sides by d^2

Either way, your main strategy should be getting d^2 by itself.

 

[CRich]

so I would have :
((pi/4)*510)/(8.25*7.6)=1/d^2 ...?

 

[Mark44]

No. The goal is to get d² all by itself on one side.
Here's where you're starting from:
$$\frac{510}{7.6} = \frac{8.25}{(\pi/4) d^2}$$

The simplest thing to do is to take the reciprocals of both sides, as pinu7 suggested (the idea is that, if a/b = c/d, then b/a = d/c).

After that, it should be a relatively simple matter to isolate the d² factor. The final step would be taking the square root of both sides, keeping in mind that d can have two values: one positive and one negative.

 

[CRich]

okay so I would have sqr((8.25*7.6)/((PI/4))*510)=d

 

[Mark44]

Yes, but again there are mathematically two possible values for d, although the negative value might not be relevant for your problem.

 

[CRich]

Okay...thx the ans is going to be positive b/c it is a force...thx for all yall's help

 

[CRich]

okay so I'm home now and I've tried what was suggested but, I still don't get the right ans...:
510/1.75=8.30/(pi/4)*d^2

I used the reciprocals and got 1.75/510=(pi/4)*d^2/8.30 ... reduced and I got
sqr root (4*8.30*1.75/pi510)=d ans:.5982 the book ans is 6.02... where did I go wrong?

 

[CRich]

nevermind I got it... I didn't make all the units match