Answer:

Step-by-step explanation:
<u>Two-Variable Functions</u>
A function expresses the relation between two variables in such a way that for each input for the independent variable n, there one and only one value for the function h(n). If it's explicitly given as an equation, then we can use values for n as we wish, and compute the different values of h(n).
The question provides the following function

We are required to find h(2), which can be computed by replacing n by the value of 2



Step-by-step explanation:
This the solution
the answer is one
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:

Lines BC, AB, and then AC
Answer:
She made an error when using the zero pair.
Step-by-step explanation:
In step 2, Carianne added 4 to the right side and subtracted 4 on the left side, which is completely changing the equation. By definition, your zero pair must have a difference of zero. She need to add 4 to both sides to continue; when manipulating algebra you need to do the same thing to both sides of an equation, otherwise you're just changing the equation.