Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x
we need to find the minimum value of z
z' = 2x + 154 which = zero for minm or maxm value
x = -77 and y = 154 -77 = 77
so the 2 numbers are -77 and 77
Answer:
See below.
Step-by-step explanation:
From the given info the 2 triangles are isosceles with AE = FR and ET = RP because the 2 sets of base angles are equal.
As the base angles are congruent m < E = m < R.
So the are 2 triangles are congruent by SAS, ASA and AAS.
The Area of the square is (side)^2
side is given to be 2^(4/9)
SO,
side^2 = [2^(4/9)]^2 = 2^(4/9 * 2) = 2^(8/9)
so the area of square is 2^(8/9) sq. inches.
The formula for an area of a regular parallelogram is:
A = l * w
Where,
l = length
w = width
We are given that the total measurement of fence is only
60 feet and one side of the house is used as one side of the pen. Therefore,
l + 2 w = 60
<span>or simplifying to make an explicit expression for
one variable, say l:</span>
l = 60 – 2 w
<span>Substituting to the 1st equation:</span>
A = (60 – 2 w) * w
A = 60 w – 2 w^2
<span>The maxima are obtained by getting the 1st
derivative then equating dA/dw = 0:</span>
dA/dw
= 60 – 4 w
60 –
4 w = 0
4 w
= 60
w =
15
Since
l = 60 - 2w
l =
60 – 30
l =
30
<span>Therefore
the dimension that will make the largest pen is 15 ft by 30 ft.</span>
<span>ANSWER: C</span>
