By simplifying both sides of the equation then isolating the variable
Answer:
W = 21.44*10⁶J
Step-by-step explanation:
Given
y = x² (0 < x < 4)
γ = 10000 N/m³
W = ?
If we apply
y = 4² = 16 = h
y = x² ⇒ x = √y
then
V = π*(√y)²*dy = π*y*dy
W = (γ*V) *(16-y) = γ*π*y*dy*(16-y)
⇒ W = γ*π*∫y*(16-y)dy = γ*π*(8y²-(y³/3))
finally we obtain (0 < y < 16)
W = γ*π*(8y²-(y³/3)) = 10000*π*(8*16²-(16³/3)) = 21.44*10⁶J
Answer:
-2x+10
Step-by-step explanation:
f(x)=5x+8
g(x)=7x-2
(f-g)(x)= 5x+8-7x+2= -2x+10
Answer:
The probability of rolling a 3 and then a 5 is 1/36.
Step-by-step explanation:
Rolling a six sided die is an independent event. That means for each roll, you have the same chance of rolling a number as the previous roll. Since there are six different numbers on a die, then there are six different outcomes for each roll - 1, 2, 3, 4, 5 or 6. The chances that you would roll a '3' is 1 out of 6, or 1/6. The chances that you would roll a '5' is also 1 out of 6, or 1/5. However, when we combine these events, we need to take each probability and multiply them. So, the probability of rolling a '3' and then a '5' is 1/6 x 1/6 or 1/36.
