Question

The strength S of a rectangular beam varies directly as its width W and the square of its depth D, and inversely as its length L. Write an equation for this relationship.

Answer 1

y varies directly as x:

\(y = kx\)

y varies inversely as z:

\(y = \dfrac{k}{z} \)

y varies directly as the square of w:

\(y = kw^2\)

Put all those together and find your answer.

Answer 2

what do you mean? im confused

Answer 3

@mathstudent55 how to i put this into an equation

Answer 4

@mathmate

Answer 5

just bring them together Hint:- k only appears onc

Answer 6

wait how do i bring it together if k only appears once?

Answer 7

@welshfella how do i put it together if k appears once?

Answer 8

So what mathstudent55 wrote is an example. To apply it to your problem, you can see for example that
y = kx is
S = kW (for your problem).

Answer 9

oh okay

Answer 10

so the equation for the relationship will be y=kx/z

Answer 11

all i need to do is find the equation

Answer 12

So using mathstudent55's example can you figure out the others:
The strength S of a rectangular beam varies directly the square of its depth D, and
The strength S of a rectangular beam varies inversely as its length L.

Answer 13

so the strength S varies both directly to depth D and length L, i knew that but im confused on how the equation is going to be put together

Answer 14

k only appears once in the equation
also use w for width, D for depth and L for length

Answer 15

Yes, so what you should do is put them as an equation to make it easier (not word form).
For example, The strength S of a rectangular beam varies directly as its width W
becomes S = kW

Answer 16

- sorry i was called away

Answer 17

so S(w)=kW?

Answer 18

im sorry i havent learned this technique yet and my teacher needs us to answer it

Answer 19

@christina166
I find it a little difficult to follow when the expressions do not use the same notations as defined in the question.
If I try to recap what was said, then, using the given notation in
"The strength S of a rectangular beam varies directly as its width W and the square of its depth D, and inversely as its length L. Write an equation for this relationship"
we have
\(S\propto W\)
\(S\propto D^2\)
\(S\propto /L\)
then
\(S\propto WD^2/L\)
where \(\propto\) reads : "proportional to"
So it's your turn to remove the \(\propto\) and replace with a constant, as discussed earlier.

Answer 20

so the equation would end up being that but replaced with a constant

Answer 21

@mathmate so it would be \[S approxWD ^{2}/L\]

Answer 22

It's \propto is you want to use LaTex.
That would be ok, but probably your teacher wants to see a constant, usually k, as @mathstudent55 did in the first place.

Answer 23

so it would then be SkWD^2/L

Answer 24

THANK YOU !!!

Answer 25

Would be perfect if there is an equal sign after "S".

Answer 26

You're welcome!

Answer 27

yes S=kWD^2/L

Answer 28

OMG THANKS!!!!!!!!!!!!

Answer 29

Yep, like that!

Answer 30

If it varies directly as a variable, write the variable in the numerator.
If it varies directly as the square of the variable, write the square of the variable in the numerator.
If it varies inversely as a variable, write the variable in the denominator.
Then include a constant of proportionality, such as k.

\(\large S = \dfrac{kWD^2}{L} \)