<span> -14x + 11y = 23
+2(7x - 3y = 37)
----------------------
0 + 5y = 97
y = 97/5
y = 19.4
7x - 3(19.4) = 37
7x - 58.2 = 37
7x = 37 + 58.2
7x = 95.2
x = 95.2/7
x = 13.6
Check
-14(13.6) + 11(19.4) = 23
-190.4 + 213.4 = 23
</span>
Answer:
Step-by-step explanation:
Answer:
The area is growing at a rate of 
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3
and we identify such as the following differential rate:

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find
.
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

We now apply the derivative operator with respect to time (
) to this equation, and use chain rule as we find the quadratic form of the radius:
![\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5BA%3D%5Cpi%5C%2Cr%5E2%5D%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%5Cpi%5C%2C%2A2%2Ar%2A%5Cfrac%7Bdr%7D%7Bdt%7D)
Now we replace the known values of the rate at which the radius is growing (
), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

which we can round to one decimal place as:
