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See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
Answer: 339/8788= 0.039
Step-by-step explanation:
Let black card be represented with B and the red card be represented with r. Therefore, P(B,r) is the expected value.
Hence, we say, (b,r) is not equal to (0,0) for the first state, we then, have a probability of B/r+B(the probability of drawing out a black card and loosing a point.
Also, (B-1,r) state with the probability of r/r+B(which is the probability of drawing out a red card and gaining a point).
The expected value is therefore;
B/r+B(-1+(B-1,r) + r/r+B(1+P(B,r-1))
Therefore, if we have negative, then;
P(B,r)=0,B/r+B(-1,r)) + r/r+B(1+P(B,r-1))...
P(0,0)=0; P(26,26) = 339/8788
=.039
Note: we say that the expectation at the start if we draw red,gaining +1 and if we draw black and then draw two reds you end +1. That is; 1/26 × 2/26 × 1/26 = 1+ 338/8788
= 339/8788.
