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marysya [2.9K]
3 years ago
8

Suppose that a varies inversely with b^2. If a=9 when b=2, find the value of a when b=3.

Mathematics
1 answer:
Archy [21]3 years ago
4 0

Answer:

a = 4

Step-by-step explanation:

We can set up an equation to model this:

a = \frac{k}{b^2}

Now, we can plug in the information given to find the value of k:

9 = \frac{k}{2^2}

9 = \frac{k}{4}

36 = k

Now, we can find the value of a when b = 3.

a = \frac{36}{3^2}

a = \frac{36}{9}

a = 4

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What do I do to figure out this problem:<br>3x+8=26+x
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<span><u>3x + 8 = 26 + x</u>

The first thing you need to do is understand what you're looking for ...
what a 'solution' means, what it looks like, and how you even know
when you have it.    I'm not sure you're there yet.

The 'answer' or the 'solution' to the problem is a number.  It's the number
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To find it, you can do anything you want to either side of the problem, as long as
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to 'figure out the problem', and find the answer:

The original problem:      </span><span><u>3x + 8 = 26 + x</u>

Subtract 8 from each side:

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Subtract 'x' from each side:

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Divide each side by 2 :

<u>x = 9 </u> .

That's what the answer looks like, and that's what the answer is.

' 9 ' is the ONLY number you can write in place of 'x' in the problem,
and have the problem read true.

I'll show you what I mean.  Let's take the original problem

                   </span><span> <u><span>3x + 8 = 26 + x

</span></u><span>and let's write ' 2 ' wherever we see 'x' :

3 (2) + 8 = 26 + 2

3 (2) means 3 times 2, and that's 6 .
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6 + 8 = 26 + 2

Do the addition on each side, and we have

14 = 28 .

That's nonsense.  14 is not equal to 28 .  The reason that happened
is because we put the wrong number in place of 'x' .  When we put the
correct number in place of 'x', the left side will be equal to the right side.
To 'figure out the problem' means to find out what that number must be.
For this particular problem, it's 9 .
</span><u><span /></u>

</span>

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