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
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Answer:
B. 200 doses
Step-by-step explanation:
Given,
1 dose is required for 100 mg,
Since, 1 mg = 0.001 g,
⇒ 100 mg = 0.1 g
⇒ 1 dost is required for 0.1 g,
Thus, the ratio of doses and quantity ( in gram ) is 
Let x be the doses required for 20 grams,
So, the ratio of doses and quantity is 
Hence, 200 doses can be obtained from 20 grams of the drug.
Option 'B' is correct.
Answer:
8x+6
Step-by-step explanation:
To simplify it, the first thing you want to do is distribute the three.
So
3(x+2) = 3x+6,
So we can then add the 5x to it.
3x+6+5x
Then, Combine Like Terms
8x+6
Answer: D) vertical angles theorem, alternate interior angles theorem
Angle 5 = Angle 6 by the alternate interior angles theorem
Angle 5 = angle 4 by the vertical angles theorem
By the transitive property, we can then say angle 4 = angle 6. These angles are also corresponding angles.
We won't use the angle addition theorem or the right angles theorem.
