Answer:
125000 square feet
Step-by-step explanation:
Since there are only three sides of the rectangle, the perimeter of the fence is:
Let x and y be the sides of the rectangle, we are left with:
2 * x + y = 1000
solving for and:
y = 1000 - 2 * x
The area of the corral is:
A = x * y
replacing
A = x * (1000 - 2*x)
A = 1000 * x - 2*x^2
to find the maximum for the parabolic function A = 1000 * x - 2*x^2
The function has a maximum since the quotient before x ^ 2 is negative: -2 <0
Amax = c - b^2 /4*a
where a = -2, b = 1000, c = 0
A max = 0 - 1000^2/(4 * (- 2))
A max = 125000 ft^2
The maximum possible area of the pen is 125000 square feet.
Notice that
• <em>π</em>/2 = <em>π</em>/3 + <em>π</em>/6
• <em>π</em>/6 = <em>π</em>/3 - <em>π</em>/6
Recall the angle sum identities for sine:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
sin(<em>x</em> - <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) - cos(<em>x</em>) sin(<em>y</em>)
By adding these together, we get
sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>) = 2 sin(<em>x</em>) cos(<em>y</em>)
==> sin(<em>x</em>) cos(<em>y</em>) = 1/2 (sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>))
Now take <em>x</em> = <em>π</em>/3 and <em>y</em> = <em>π</em>/6 :
sin(<em>π</em>/3) cos(<em>π</em>/6) = 1/2 (sin(<em>π</em>/2) + sin(<em>π</em>/6))
So the blank should be filled with cos.
1. slope of the given line = 1/5
the equation is
(y-2)/(x-(-2))=1/5
x+2=5y-10
x-5y+12=0
2. slope of the given line = -1/6
the equation is
(y-9)/x=6
y-9=6x
y=6x+9
Do you have a picture, I need one to help you, otherwise I can’t.
