Answer:
V = 128π/3 vu
Step-by-step explanation:
we have that: f(x)₁ = √(4 - x²); f(x)₂ = -√(4 - x²)
knowing that the volume of a solid is V=πR²h, where R² (f(x)₁-f(x)₂) and h=dx, then
dV=π(√(4 - x²)+√(4 - x²))²dx; =π(2√(4 - x²))²dx ⇒
dV= 4π(4-x²)dx , Integrating in both sides
∫dv=4π∫(4-x²)dx , we take ∫(4-x²)dx and we solve
4∫dx-∫x²dx = 4x-(x³/3) evaluated -2≤x≤2 or too 2 (0≤x≤2) , also
∫dv=8π∫(4-x²)dx evaluated 0≤x≤2
V=8π(4x-(x³/3)) = 8π(4.2-(2³/3)) = 8π(8-(8/3)) =(8π/3)(24-8) ⇒
V = 128π/3 vu
The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be:
<em><u>Explanation</u></em>
In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.
If represents the year and
represents the number of students, then two points in form of
will be:
and
So, the rate of change or slope = (change in value of y / change in value of x)
Now, plugging slope = 20 and first point
into <u>point slope form of linear equation</u>
, we will get.....