Answer:
8
Step-by-step explanation:
A heavy bank-vault door is opened by the application of a force of 3.0 x 102 N directed perpendicular to the plane of the door a
1 answer:
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Answer:
The width is 3cm, and the length is 7cm.
Step-by-step explanation:
Let's call the length of the rectangle , the width of the rectangle
, and the area of the rectangle
, and write down everything we know about them.
The length of the rectangle is 11 centimetres less than six times its width, so we know that .
We also know that . But what exactly is the area of a rectangle? Well, it's the product of its length and width, <em>i.e. </em>
<em>.</em>
Then we have two equations involving and
:
, and
.
So how do we find and
? Let's substitute our first equation into our second, like so:
We can rearrange this new equation to get everything on the same side, so that we have a standard quadratic equation, like this:
.
We can use the quadratic formula for this. You should have seen this before:
,
where are the coefficients of our quadratic equation. Plugging the values in, we see
.
With a little further cancellation, we can find our two possible values of are
and
.
Since is a width of a rectangle, it can't possibly be negative, and so it must be 3.
We can now plug in this value into our equation from earlier, namely . We can see that
,
and so we get our answer, cm,
cm.
We can prove that this is right by multiply 3 and 7 together, and seeing that we get 21, the area we expect.