0

Question: given that $B^2$ is inversely proportional to $A+3$ and $B$ is always positive, find the value of $B$ when $A=17$ if $B=5$ when $A=2$.

I am so confused on how to work out this question. I know this is a pretty easy question to all of you. But I find this very confusing. Can someone explain to me what I need to do and how I do it ?

Sorry for the nooby question.

Olórin
  • 12,040
user215301
  • 3

3 Answers3

2

Saying $B^2$ is inversely proportional to $A+3$ means $B^2=\frac k{A+3}$ or $B^2(A+3)=k$. You are give a data point, $A=2,B=5$, which lets you evaluate $k$. Then plug in $A=17$ and evaluate $B$.

Ross Millikan
  • 374,822
0

Inverse proportion means that $B^2 * (A + 3) = k$.

When dealing with these kinds of questions, you are basically doing the following:

Substitute $k$ with the same inverse proportion but different values.

So, $B_1^2 * (A_1 + 3) = B_2^2 * (A_2 + 3)$. We'll plug in for $B_2, A_2, A_1$ and solve for $B_1$.

$B_1^2 * (17 + 3) = 5^2 * (2 + 3)$

So, we get $B_1^2 * 20 = 125 \to B_1^2 = \frac{125}{20} \to B_1 = \sqrt{\frac{125}{20}}$, and then you just take the positive of that square root (it'll give you positive anyways, so you're set.)

David
  • 1,094
  • How'd you know to multiply 5^2 * (2+3). Like how did you know you had to do that? – user215301 Feb 15 '15 at 15:13
  • So, we know that $B^2 * (A + 3) = k$. If we use $B = 5, A = 2$, then we see that $5^2 * (2 + 3) = 125$ because we're substituting in $B$ and $A$. Once we have 125,we know $k$, and $A$ because they tell us that $A = 17$. So, if you go back you see $B^2 * (17 + 3) = 125$ and then you solve for $B$. Essentially, inverse proportion means that as $A$ grows, $B$ shrinks. We know how $B$ and $A$ are related based on $B^2 * (A + 3)$. When someone gives us other values of $B$ and $A$ like $B = 5, A = 2$ we're given an actual point to base calculations off of. Which is how we know $B$ for $A = 17$. – David Feb 15 '15 at 15:17
  • I like to think of $k$ as the Constant of Proportionality. So, if we're given a point $B = 5, A = 2$, then they'll give us a Constant of Proportionality, $k$, that relates them somehow. Once we know $k$, we can figure out the respective $B$ or $A$ for any pair. Once you know $k$ relative to a $B, A$ pair you can ask "I wonder what $B$ will be for $A = 10$" or "I wonder what $A$ will be for $B = 15$". – David Feb 15 '15 at 15:21
  • Thanks for all the help man! I really appreciate it :) – user215301 Feb 15 '15 at 15:22
0

Let B^2 = k/(A+3) where k is proportionality constant. at A = 2, B =5 so 5^2 = k/(2+3) or K = 5^3 = 125 Now at A = 17 B^2 = 125/(17+3) = 125/20 = 25/4 so B = 5/2

I hope it will help.

Kouts Km
  • 66