Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.
Then, the perimeter is given by
4
x
+
3
y
=
160
.
4
x
=
160
−
3
y
x
=
40
−
3
4
y
The area of a rectangle is given by
A
=
L
×
W
, however here we have two rectangles put together, so the total area will be given by
A
=
2
×
L
×
W
.
A
=
2
(
40
−
3
4
y
)
y
A
=
80
y
−
3
2
y
2
Now, let's differentiate this function, with respect to y, to find any critical points on the graph.
A
'
(
y
)
=
80
−
3
y
Setting to 0:
0
=
80
−
3
y
−
80
=
−
3
y
80
3
=
y
x
=
40
−
3
4
×
80
3
x
=
40
−
20
x
=
20
Hence, the dimensions that will give the maximum area are
20
by
26
2
3
feet.
A graphical check of the initial function shows that the vertex is at
(
26
2
3
,
1066
2
3
)
, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.
Hopefully this helps!
Step-by-step explanation: hope this helps
Answer:
D. 30
Step-by-step explanation:
At the center of the polygon are twelve 30° angles - 360° / 12.If the polygon is rotated 30° the image (transformation) shall coincide with the preimage (the figure before transformation).
<u>Answer:</u>
<u>ii) £120</u>
<u>iii) £2,400</u>
<u>a) 10 workers</u>
<u>c) 4 workers more to be employed.</u>
<u>Step-by-step explanation:</u>
ii) To find the buying price we deduct 20% (percent) from the selling price of £150.
= 20/100 x 150
= £30 (Next we substract this value from the selling price of £150) = €150 - £30 = £120
iii) A 12% interest per annum Implies a 12 percent of the borrowed amount of 20,000, which is calculated as
12% or 12/100 x 20,000 = £2,400
a) Put simply, we create an equation for the problem.
4 men * 10 days = 40 man days.
X men * 4 days = 40 man days.
Let's substitute the equation:
(X/ 4) * (4/ 10) = 40 / 40
(X/4) * 0.4= 1 (collect like terms)
0.4 * x = 4
0.4x/0.4= 4/0.4
x = 10 workers.
(c) 4 extra workers to would need to be employed since we have six already available (10-6=4).
D the slope for function A one is -2 and the slope for function B is 4
We can notice that : Line Passes through the Points (1 , 2) and (4 , -4)
Let us find the slope of the line in order to write the Equation of the Line.
Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :
Points are (1 , 2) and (4 , -4)
here x₁ = 1 and x₂ = 4 and y₁ = 2 and y₂ = -4
Equation of the Line passing through (1 , 2) and having slope -2 is :
⇒ y - 2 = -2(x - 1)
⇒ y = -2x + 2 + 2
⇒ y = -2x + 4
