The volume of the resulting solid of revolution about the x-axis will be π/7 cubic units.
<h3>What is a solid revolution?</h3>
When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.
The region under the function over the interval [0,1] on the x-axis revolved about the x-axis.
f(x) = x³
Then the volume of the resulting solid of revolution will be given as
![\rm V = \int _0^1 \pi [f(x)]^2 \ dx](https://tex.z-dn.net/?f=%5Crm%20V%20%3D%20%5Cint%20_0%5E1%20%5Cpi%20%5Bf%28x%29%5D%5E2%20%5C%20dx)
Then we have
![\rm V = \int _0^1 \pi (x^3)^2 \ dx\\\\\\V = \pi \int _0^1 x^6 \ dx\\\\\\V = \dfrac{\pi}{7} \left [ x^7 \right ] _0^1\\](https://tex.z-dn.net/?f=%5Crm%20V%20%3D%20%5Cint%20_0%5E1%20%5Cpi%20%28x%5E3%29%5E2%20%5C%20dx%5C%5C%5C%5C%5C%5CV%20%3D%20%5Cpi%20%5Cint%20_0%5E1%20%20x%5E6%20%5C%20dx%5C%5C%5C%5C%5C%5CV%20%3D%20%5Cdfrac%7B%5Cpi%7D%7B7%7D%20%5Cleft%20%5B%20x%5E7%20%5Cright%20%5D%20_0%5E1%5C%5C)
V = π/7 (1⁷ - 0⁷)
V = π/7 cubic units
Then the volume of the resulting solid of revolution will be π/7 cubic units.
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Answer: 1.1%
Step-by-step explanation:
To get a percentage you want to divide the ending number by the base number
73 / 68 = 1.07
It says to round to the neartest tenth, when rounding if the number is 5 or above you round up, if under 5 your number stays the same
7 is higher than 5 so we round up
1.1%
Answer:
Step-by-step explanation:
Ok I think it is 8 though
Answer:
the most conservative hypothesis is
<em>H₀</em>: <em>p</em> = 0.18, <em>Hₐ</em>: <em>p</em> > 0.18.
Step-by-step explanation:
The researcher wants to test whether the rate of smoking among adults in Chicago is greater than the national rate of 18% or not.
The hypothesis for this test can be defined as follows:
Null Hypothesis (
): The rate of smoking among adults in Chicago is same as the national rate, i.e. <em>p</em> = 0.18.
Alternate Hypothesis (
): The rate of smoking among adults in Chicago is greater than the national rate, i.e. <em>p</em> > 0.18.
So the most conservative hypothesis is <em>H₀</em>: <em>p</em> = 0.18, <em>Hₐ</em>: <em>p</em> > 0.18.
To use an equation to predict a pattern, we substitute the value of the input variable in the equation.
<h3>What are equations?</h3>
- Equations are used to represent expressions of equal values
- Equations are represented by the "=" sign
<h3>Using equation to predict a pattern</h3>
To use an equation to predict a pattern, we simply substitute the value of the independent variable in the equation.
Take for instance, we have the following equation that represents a pattern
![y = 2x + 1](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%201)
In the above equation, we have:
- x represents the independent variable i.e. the input
- y represents the dependent variable i.e. the output
When x = 1, y = 3
When x = 2, y = 5
When x = 3, y = 7
So, a pattern from the equation could be 3, 5, 7....
Read more about equation and patterns at:
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