T.
a rectangular playground space is to be fenced in using the wall of a daycare building
for one side and 200 meters of fencing for the other three sides. the area a(x) in
square meters of the playground space is a function of the length x in meters of each of
the sides perpendicular to the wall of the daycare building.
a.
what is the area of the playground when x = 50?
b.
write an expression for a(x).
c.
what is a reasonable domain for a in this context?

We know that for a rectangle of length L and width W the area is just given by:

A = L*W.

And the perimeter is:

P  = 2*(L + W)

The solutions are:

a) 500 square meters.

b) A(x) = x*(200m - 2*x)

c) 0m < x < 100m

Here we have a rectangle of a perimeter equal to 200m + L

Where L is the side that is along the wall, and we call "x" as the length of the side perpendicular to the wall.

Then we also have:

200m = 2*x + L

a) If x = 50, we can use the above equation to find the length of the other side.

200m = 2*50m + L

200m = 100m + L

200m - 100m = L

100m = L

Then the two measures of the rectangle are:

L = 100m

x = 50m

Then the area is:

A = 100m*50m = 500m^2

b) Now we want a general expression for A(x).

We have:

A(x) = x*L

And we know that:

200m = 2*x + L

Then we can isolate L to get:

200m - 2*x  =L

Now we can replace that in the area equation:

A(x) = x*(200m - 2*x)

Now the equation only depends on the variable x, as wanted.

c) The domain of a function is the set of possible inputs that we can use.

Here, x represents the length of one of the sides of a rectangle, so we should start with:

x > 0m

So x is a positive number.

Now let's go to the equation:

200m - 2*x  =L

L is also a measure, so L also must be larger than zero meters, then we can write:

200m - 2*x > 0m

Now we can solve this for x:

200m > 2*x

200m/2 > x

100m > x

Writing together the two inequalities, we get:

0m < x < 100m

This is the domain of the area function.

If you want to learn more, you can read:

link

  a) 5000 m²

  b) A(x) = x(200 -2x)

  c) 0 < x < 100

Step-by-step explanation:

b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:

  A(x) = x(200 -2x)

__

a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²

__

c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

what's the question?

step-by-step explanation:

there is no question.