Ah, Micah, that rat.
The answer is B, I took the test and that was correct.
If you break the equation up into systems, you can see that they intersect at 0.297, which would be the solution to the systems.
Your answer is B, (1,5)
Based on your equation, 5x means in one movement of the x axis it increases 5 spaces on the Y axis. Since there is nothing after the 5x indicating it is starting elsewhere this means it starts at 0.0. So after the first movement on the x axis your value will be 1 plug in your x axis value to the equation f(x)=5x so it will look like f(1)=5•1 and then you will have both values needed to form your answer (1,5)
Well, the problem is that he does not replace the first marble after he draws it. Therefore, yes, he has a 2/12 probability of drawing a yellow marble first, but then he has a 4/11 probability of drawing a red marble second, not 4/12. This is because there are going to only be 11 marbles left in the bag after he draws the first marble and does not replace it.
The correct answer would be:
(2/12)(4/11)=8/132=4/66=2/33
Answer: 1/30
Step-by-step explanation:
∫[0,4] arcsin(x/4) dx = 2π-4
x = 4sin(u)
arcsin(x/4) = arcsin(sin(u)) = u
dx = 4cos(u) du
∫[0,4] 4u cos(u) du
∫[0,4] f(x) dx = ∫[0,π/2] g(u) du
v = ∫[1,e] π(R^2-r^2) dx
where R=2 and r=lnx+1
v = ∫[1,e] π(4-(lnx + 1)^2) dx
Using shells dy
v = ∫[0,1] 2πrh dy
where r = y+1 and h=x-1=e^y-1
v = ∫[0,1] 2π(y+1)(e^y-1) dy
v = ∫[0,1] (x-x^2)^2 dx = 1/30
