The answer is (3600 - 900π) ft²
Step 1. Find the radius r of circles.
Step 2. Find the area of the portion of the field that will be watered by the sprinklers (A1)
Step 3. Find the total area of the field (A2)
Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A)
Step 1. Find the radius r of circles
r = ?
According to the image, radius of a square is one fourth of the field side length:
r = s/4
s = 60 ft
r = 60/4 = 15 ft
Step 2. Find the area of the portion of the field that will be watered by the sprinklers.
The area of the field that will be watered by the sprinklers (A1) is actually total area of 4 circles with radius 15 ft.
Since the area of a circle is π r², then A1 is:
A1 = 4 * π r² = 4 * π * 15² = 900π ft²
Step 3. Find the total area of the field (A2)
The field is actually a square with side s = 60 ft.
A2 = s² = 60² = 3600 ft²
Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A).
To get the area of the portion of the field that will not be watered by the sprinklers (A) we need to subtract the area of 4 circles from the total area:
A = A2 - A1
A = (3600 - 900π) ft²
Answer:
2(x - 7)(x + 2)
Step-by-step explanation:
Given
2x² - 10x - 28 ← factor out 2 from each term
= 2(x² - 5x - 14) ← factor the quadratic
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2 , since
- 7 × 2 = - 14 and - 7 + 2 = - 5 , thus
x² - 5x - 14 = (x - 7)(x + 2) and
2x² - 10x - 28 = 2(x - 7)(x + 2)
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
12=2x6 or 12=6x2 either way it should be the same I hope this helps
To get standard form we need to move variables with their coefficients on one side and numbers on other side. Standard form looks like this:
Ax + By = C
y - 4 = 3x/4 +6
y - 3x/4 = 6+4
y - 3x/4 = 10
