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:
f(-4)= 24
Step-by-step explanation:
-4(-4)+8 We need to multiply -4 and -4 and a negative times a negative is a positive.
16+8 Now it's easy math and we just add them
This gives us 24.
Answer:
The function is represented by 
.
Step-by-step explanation:
In this case, we must observe that total cost of the dog (
) is the sum of two components: i) <em>Fixed cost</em> (
) - Adoption fee, ii) <em>Variable cost</em> (
) - Daily cost of feeding the dog, both measured in US dollars.
In addition, we suppose that variable cost is directly proportional to the number of days that Kirstin owns her dog. That is:
Where:
- Number of days that Kirstin owns her dog, measured in days.
- Daily feeding costs, measured in US dollars per day.
If 
, then:
The function is represented by .
Use Pythagorean theorem.
[tex]|ON|^2+|MN|^2=|OM|^2\\\\x^2+x^2=8^2\\\\2x^2=64\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=32\to x=\sqrt{32}\\\\x=\sqrt{16\cdot2}\\\\x=\sqrt{16}\cdot\sqrt2\\\\\boxed{x=4\sqrt2}
Answer: |MN| = 4√2.
Hello! So, the train travels 80 miles in an hour. 90 minutes is equivalent ot 1 ½ hours. In case you don't know, ½ of 80 is 40. To find the distance gone in 90 minutes, we can just add 80 and 40. 80 + 40 is 120. Another way to solve it is to multiply 80 by 1.5 and you would still get the same answer. There. The train will have gone 120 miles in 90 minutes.
