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
Answer:
91
Step-by-step explanation:
This is the distributive property; you're taking the 10 and giving it, or distributing it, to the 4 and the 3. the best way to remember it on sight is just thinking about what "distributing" means.
Answer:
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
Step-by-step explanation:
We have the following:
x = the speed of the jet in still air.
y = the speed of the wind
we know that the speed is equal to:
v = d / t
therefore the distance would be:
d = v * t
if we replace with the information of the exercise we have:
3 * (x + y) = 1095
3 * (x - y) = 987
we must solve this system of equations, add both equations and we are left:
3 * x + 3 * y = 1095
3 * x - 3 * y = 987
3 * x + 3 * y + 3 * x - 3 * y = 1095 + 987
6 * x = 2082
x = 2082/6 = 347
now to calculate y, we replace:
3 * (347 + y) = 1095
1041 + 3 * y = 1095
3 * y = 1095 - 1041
y = 54/3 = 18
The speed of the jet is 347 mph and the speed of the wind is 18 mph.