Answer:
In B, One card is chosen from a standard deck, it is set aside, then a second card is drawn. That "set aside" is where we have a problem. We began with 52 cards, but now have 51. This fact WILL change the probability or probabilities. Chances of obtaining a red heart from the full 52-card deck are 4/52; whereas chances of obtaining a red heart from the remaining 51 cards (assuming that you got a red heart earlier and set it aside) is 3/51.
Answer:
c=2
Step-by-step explanation:
All polynomials are continuous and differentiable on the set of real numbers.
So we just need to confirm on the given interval that f(1)=f(3).
f(1)=1-12(1)+3(1)^2
f(1)=1-12+3
f(1)=-8
f(3)=1-12(3)+3(3)^2
f(3)=1-36+27
f(3)=-8
So this means there is c in (1,3) such that f'(c)=0.
To solve that equation we must differentiate.
f(x)=1-12x+3x^2
f'(x)=0-12+6x
f'(x)=-12+6x
Remember we need yo solve f'(c)=0 for c.
So we need to solve -12+6c=0.
-12+6c=0
Add 12 on both sides:
6c=12
Divide both sides by 6:
c=2
Answer:
Step-by-step explanation:
Let's give this a go here. The volume formula for the shell method while rotating about a horizontal line is
where p(y) is the distance from the axis of rotation (the x-axis) to the center of the solid. This is a positive distance and it is just y.
h(y) is the horizontal height of the function. Our function starts at x = 0 and ends at the function itself, so h(y) = 3 + y^2.
In the shell method when rotating about a horizontal line, we need to use x = y equations, and y-intervals. Setting up our integral then:
We can simplify this a bit by distributing the y into the parenthesis:
Integrating gives us
from 2 to 3
Using the First Fundamental Theorem of Calculus:
![V=2\pi[\frac{135}{4}-\frac{40}{4}]](https://tex.z-dn.net/?f=V%3D2%5Cpi%5B%5Cfrac%7B135%7D%7B4%7D-%5Cfrac%7B40%7D%7B4%7D%5D)
which simplifies down to
Answer:
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