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
If you would like to write x = 1/3 * y in general form, you can do this using the following steps:
The general form of the equation is: ax + by + c = 0.
x = 1/3 * y
x - 1/3 * y = 0
The correct result would be x - 1/3 * y = 0.
Answer:
x^2 - 5x = 14
x^2 - 5x-14 = 0
Now, we have to find the multiples of -14 and numbers that add/subtract to -5; this helps to find the factors.
-7+2 = -5
-7*2 = -14
Based on the above info, we can find out my factors; they are:-
(x-7)(x+2)
