The area is:
A = x * y
The perimeter is:
P = 2x + 2y = 100
We clear y:
2y = 100-2x
y = 50-x
We write the area in terms of x:
A (x) = x * (50-x)
Rewriting:
A (x) = 50x-x ^ 2
Deriving:
A '(x) = 50-2x
We equal zero and clear x:
50-2x = 0
x = 50/2
x = 25
Then, the other dimension is given by:
y = 50-x
y = 50-25
y = 25
Therefore, the largest area is:
A = (25) * (25)
A = 625 feet ^ 2
Answer:
the largest area you can enclose using the materials you have is:
A = 625 feet ^ 2
X²+15x+36<0
at first solve quadratic equation
D=b²-4ac= 225-4*1*36= 81
x=(-b+/-√D)/2a
x=(-15+/-√81)/2= (-15+/-9)/2
x1=(-15-9)/2=-12
x2=(-15+9)/2=-3
we can write x²+15x+36<0 as (x+12)(x+3)<0
(x+12)(x+3)<0 can be 2 cases, because for product to be negative one factor should be negative , and second factor should be positive
1 case) x+12<0, and x+3>0,
x<-12, and x>-3
(-∞, -12) and(-3,∞) gives empty set
or second case) x+12>0 and x+3<0
x>-12 and x<-3
(-12,∞) and (-∞,-3) they are crossing , so (-12, -3) is a solution of this inequality
3323.5 because if you times the number left by the 15 percent this is the answer.
I hope this helps you
y+z=4-x
5x+4-x=16
4x=12
x=3
x+y+z+x-y+4z=4+27
2x+5z=31
2.3+5z=31
5z=25
z=5
x+y+z=4
3+y+5=4
y=-4