Answer:
V=25088π vu
Step-by-step explanation:
Because the curves are a function of "y" it is decided to take the axis of rotation as y
, according to the graph 1 the cutoff points of f(y)₁ and f(y)₂ are ±2
f(y)₁ = 7y²-28; f(y)₂=28-7y²
y=0; x=28-0 ⇒ x=28
x=0; 0 = 7y²-28 ⇒ 7y²=28 ⇒ y²= 28/7 =4 ⇒ y=√4 =±2
Knowing that the volume of a solid of revolution V=πR²h, where R²=(r₁-r₂) and h=dy then:
dV=π(7y²-28-(28-7y²))²dy ⇒dV=π(7y²-28-28+7y²)²dy = 4π(7y²-28)²dy
dV=4π(49y⁴-392y²+784)dy integrating on both sides
∫dV=4π∫(49y⁴-392y²+784)dy ⇒ solving ∫(49y⁴-392y²+784)dy
49∫y⁴dy-392∫y²dy+784∫dy =
V=4π( 
) evaluated -2≤y≤2, or 2(0≤y≤2), also
⇒ V=25088π vu
Answer:
d. 3x³ and 2x³
Step-by-step explanation:
In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.
Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.
9514 1404 393
Answer:
1.1 quarts
Step-by-step explanation:
Let x represent the amount to be added, in quarts. Then the amount of anti-freeze in the resulting solution is ...
0.20(8) + 1.00(x) = 0.30(8 +x)
0.70x = 0.10(8) . . . . . . subtract 0.20(8)+0.30(x)
x = 8/7 . . . . . . . . . . . . . divide by the coefficient of x
x ≈ 1.142857 ≈ 1.1
About 1.1 quarts of pure antifreeze must be added.
Answer: I will do this from top to bottom.
Step-by-step explanation:
1. -36.8+9.2x
2. The equation is incorrect so tell me the right equation.
3. -18.4
The number of fish decreases by x% each year. x% can also be written as 0.01x.
If the total number of fish in a lake is A, after one year the number of fish will be:
After two years the number of fish will be:
So, the general formula for the number of fish after n years can be written as:
It is given that after 8 years, the number of fish is reduced to half. So we can write:
This means the value of x is 8.3%. So, the number of fish in a lake decreases by 8.3% each year
