<h2>
Answer:</h2>
<u>The length is</u><u> 12 feet</u>
<h2>
Step-by-step explanation:</h2>
The width of the garden is 5 feet
After that the total edging is telling us the area
We know that
<h3>Area of rectangle = length x width</h3>
So
60 = length x 5
Length = 60 / 5
Length = 12 feet
Multiply 2/3 by the reciprocal, 3/2, on both sides.
Answer:
a) ⅓ units²
b) 4/15 pi units³
c) 2/3 pi units³
Step-by-step explanation:
4y = x²
2y = x
4y = (2y)²
4y = 4y²
4y² - 4y = 0
y(y-1) = 0
y = 0, 1
x = 0, 2
Area
Integrate: x²/4 - x/2
From 0 to 2
(x³/12 - x²/4)
(8/12 - 4/4) - 0
= -⅓
Area = ⅓
Volume:
Squares and then integrate
Integrate: [x²/4]² - [x/2]²
Integrate: x⁴/16 - x²/4
x⁵/80 - x³/12
Limits 0 to 2
(2⁵/80 - 2³/12) - 0
-4/15
Volume = 4/15 pi
About the x-axis
x² = 4y
x² = 4y²
Integrate the difference
Integrate: 4y² - 4y
4y³/3 - 2y²
Limits 0 to 1
(4/3 - 2) - 0
-2/3
Volume = ⅔ pi
Answer: Neither
The function is not even because it doesn't have y axis symmetry. In other words, reflecting it over the vertical y axis means it doesn't line up with itself. The left half is different from the right half.
The function isn't odd either. Why not? Because rotating it 180 degrees around the origin has the function curve looking completely different. A point like (3,6) will rotate to (-3,-6) which is not on the orange curve. This is just one counter-example as to why the function is not odd.
The reflection across x = -2 will be x = 2.