<h3><u>Question:</u></h3>
Serena uses chalk to draw a straight line on the sidewalk. The line is 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?
<h3><u>Answer:</u></h3>
The number of sections that the line is divided is 4
<h3><u>Solution:</u></h3>
Given that, Serena uses chalk to draw a straight line on the sidewalk
The line is 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long
From given,
![Total\ length\ of\ line = \frac{1}{2} \text{ feet }\\\\Length\ of\ each\ section = \frac{1}{8} \text{ feet }](https://tex.z-dn.net/?f=Total%5C%20length%5C%20of%5C%20line%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctext%7B%20feet%20%7D%5C%5C%5C%5CLength%5C%20of%5C%20each%5C%20section%20%3D%20%5Cfrac%7B1%7D%7B8%7D%20%5Ctext%7B%20feet%20%7D)
To find: Number of sections can be made
The number of sections that can be made is found by dividing the total length of line by length of each section
![\text{Number of sections } = \frac{\text{Total length of line}}{\text{length of each section}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20sections%20%7D%20%3D%20%5Cfrac%7B%5Ctext%7BTotal%20length%20of%20line%7D%7D%7B%5Ctext%7Blength%20of%20each%20section%7D%7D)
Substituting the values, we get,
![\text{Number of sections } = \frac{\frac{1}{2}}{\frac{1}{8}}\\\\\text{Number of sections } = \frac{1}{2} \times \frac{8}{1}\\\\\text{Number of sections } = 4](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20sections%20%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B1%7D%7B8%7D%7D%5C%5C%5C%5C%5Ctext%7BNumber%20of%20sections%20%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B8%7D%7B1%7D%5C%5C%5C%5C%5Ctext%7BNumber%20of%20sections%20%7D%20%3D%204)
Thus number of sections that the line is divided is 4
Step-by-step explanation:
No, the LaTeX that the app uses starts and ends with the [ tex ] and [/ tex ] tags (without the spaces). In (1), simply remove the \latex tag and the integral will appear in embedded form:
![\int_a^b f(x)\, dx](https://tex.z-dn.net/?f=%20%5Cint_a%5Eb%20f%28x%29%5C%2C%20dx)
This is meant to maintain the line spacing. If you want show the full size of the integral (or in display mode), add the \displaystyle tag after the [ tex ] like this
[ tex ]\displaystyle \int_a^b f(x)\, dx[/ tex ]
and the integral will look like this
![\displaystyle \int_a^b f(x)\, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_a%5Eb%20f%28x%29%5C%2C%20dx)
after removing the spaces in the [tex] tag. This works also for sums and product of a series and limits.
Answer:
Therefore,
Volume of the cylinder is 24501.42 m³.
Step-by-step explanation:
Given:
Height of Cylinder = 27 m
Diameter, d = 34 m
![Radius = \dfrac{d}{2}=\dfrac{34}{2}=17\ m](https://tex.z-dn.net/?f=Radius%20%3D%20%5Cdfrac%7Bd%7D%7B2%7D%3D%5Cdfrac%7B34%7D%7B2%7D%3D17%5C%20m)
Volume of a Cylinder = ?
Solution:
We know that
![\textrm{Volume of a Cylinder}=\pi (Radius)^{2}\times Height](https://tex.z-dn.net/?f=%5Ctextrm%7BVolume%20of%20a%20Cylinder%7D%3D%5Cpi%20%28Radius%29%5E%7B2%7D%5Ctimes%20Height)
Substituting the given values in formula we get
![\textrm{Volume of a Cylinder}=3.14 (17)^{2}\times 27=24501.42\ m^{3}](https://tex.z-dn.net/?f=%5Ctextrm%7BVolume%20of%20a%20Cylinder%7D%3D3.14%20%2817%29%5E%7B2%7D%5Ctimes%2027%3D24501.42%5C%20m%5E%7B3%7D)
Therefore,
Volume of the cylinder is 24501.42 m³.
Answer:
If we used the quadratic formula to solve the equation we can say:
-b = -5
b² - 4ac = 13
2a = 2
Solving the first and last equations we get b = 5 and a = 1. Substituting these values into the second equation we get:
25 - 4c = 13
Solving this we get c = 3 so the answer is x² + 5x + 3.