Answer:
The dimensions of the yard are W=20ft and L=40ft.
Step-by-step explanation:
Let be:
W: width of the yard.
L:length.
Now, we can write the equation of that relates length and width:
(Equation #1)
The area of the yard can be expressed as (using equation #1 into #2):
(Equation #2)
Since the Area of the yard is 
, then equation #2 turns into:
Now, we rearrange this equation:
We can divide the equation by 5 :
We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since 
and 
. The equation factorised looks like this:
Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:
Therefore, the dimensions of the yard are W=20ft and L=40ft.
General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace 
for f(x) in the above inequality to find the domain.
![-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0](https://tex.z-dn.net/?f=%20-15x%5E2%2B6000%5Cgeq%200%20%5C%3B%20%5C%3B%20%20%5BDivide%20%5C%3B%20by%5C%3B%20-15%5C%3B%20on%5C%3B%20both%5C%3B%20sides%5D%5C%5C%20%5C%5C%20%5Cfrac%7B-15x%5E2%7D%7B-15%7D%20%2B%5Cfrac%7B6000%7D%7B-15%7D%20%5Cleq%20%5Cfrac%7B0%7D%7B-15%7D%20%5C%5C%20%5C%5C%20x%5E2-400%5Cleq%200%5C%3B%5BFactoring%5C%3Bon%5C%3Bleft%5C%3Bside%5D%5C%5C%20%5C%5C%20%28x%2B200%29%28x-200%29%5Cleq%200%20)
The possible solutions of the above inequality are given by the intervals ![(-\infty , -2], [-2,2], [2,\infty )](https://tex.z-dn.net/?f=%20%28-%5Cinfty%20%2C%20-2%5D%2C%20%5B-2%2C2%5D%2C%20%5B2%2C%5Cinfty%20%29%20)
. We need to pick test point from each possible solution interval and check whether that test point make the inequality 
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is 
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is 
We know that
<span>the isosceles triangle has two equal sides
</span>
<span>let's analyze two cases
</span>
first case
perimeter=22 cm
<span>let's suppose that the known side of 6 cm is one of the two equal sides
</span>perimeter=6+6+x
22=6+6+x-----> x=22-12----> x=10 cm
answer first case
<span>the possible lengths of the other two sides are
</span>6 cm
10 cm
second case
let's suppose that the known side of 6 cm is the side that is not equal
perimeter=22 cm
perimeter=6+x+x
22=6+x+x----> 2x=22-6----> 2x=16-----> x=8 cm
answer second case
the possible lengths of the other two sides are
8 cm
8 cm
11 minutes has passed just subtract
