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
The smallest of the three consecutive integers is 24.
<h3>How to solve algebraic word problems?</h3>
Let the 3 consecutive integers be;
x, y and z
Thus;
y = x + 1
z = x + 2
Now, we are told that their sum is equal to 4 times the largest number minus 29. Thus;
x + x + 1 + x + 2 = 4(x + 2) - 29
3x + 3 = 4x + 8 - 29
4x - 3x = 3 + 21
x = 24
Thus, we can conclude that the smallest of the three consecutive integers is 24.
Read more about algebra word problems at; brainly.com/question/13818690
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Sample space of two fair 6 sided dice is 36.
Product = perfect square are (1, 1), (1, 4), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Probability that their product is perfect square = 7/36
