It is stated that a straight rod has one endpoint at the origin (0,0) and the opposite endpoint at (L,0), with a linear density defined by 
, where a is a constant and x is the x coordinate.
Thus, the infinitesimal mass is expressed as:
The total mass can be calculated by integrating the above expression as follows:
Consequently, ![m=a\int\limits^L_0 {x^2} \, dx=a[\frac{x^3}{3}]_{0}^{L}=\frac{a}{3}[L^3-0]= \frac{aL^3}{3}](https://tex.z-dn.net/?f=m%3Da%5Cint%5Climits%5EL_0%20%7Bx%5E2%7D%20%5C%2C%20dx%3Da%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5D_%7B0%7D%5E%7BL%7D%3D%5Cfrac%7Ba%7D%7B3%7D%5BL%5E3-0%5D%3D%20%5Cfrac%7BaL%5E3%7D%7B3%7D)
Now, we can calculate the center of mass, 
of the rod as:
Now, it follows that
x_{cm}=\frac{1}{\frac{aL^3}{3}}\int_{0}^{L}ax^3dx=\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}
Therefore, the center of mass, is located at:
![\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}=\frac{3}{aL^3}\times \frac{aL^4}{4}=\frac{3}{4}L](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7BaL%5E3%7D%5Ctimes%20%5B%5Cfrac%7Bax%5E4%7D%7B4%7D%5D_%7B0%7D%5E%7BL%7D%3D%5Cfrac%7B3%7D%7BaL%5E3%7D%5Ctimes%20%5Cfrac%7BaL%5E4%7D%7B4%7D%3D%5Cfrac%7B3%7D%7B4%7DL)
Answer:
zero slope
Step-by-step explanation:
Hope this information is helpful:)
There are 0.015 kilograms in 15 grams. Since each can weighs 0.015 kg and the payment rate is 50p per kilogram, 0.015 multiplied by 66 amounts to 1 kilogram! Therefore, 66 cans are needed to generate one kilogram. As a result, earning £15 would mean that with 2 kg equating to one dollar, then 15 multiplied by 2 equals 30. Consequently, 66 times 30 gives 1980!
66 relates to each kilogram, and 30 indicates how many 50p are required for one dollar!
Thus, to obtain £15, Adam has to recycle a total of 1980 cans!
<span>Determine the configuration of columns and rows for the rectangular arrangement of 120 cupcakes.
=> There must be an even number of rows and an odd number of columns.
=> 120 = 2 x 2 x 2 x 15
=> 120 = 8 x 15
=> 120 = 120
Consequently, the glee club should organize the cupcakes in 8 rows and 15 columns.
This totals up to 120 cupcakes altogether.
</span>
Quadratic equations find their application in various real-world scenarios such as: sports, bridges, projectile motion, the curvature of bananas, and so on.
Here are three images representing real-world instances of quadratics:
Example 1: A cyclist travels along a parabolic trajectory to leap over obstacles.
Example 2: A person throws a basketball towards the hoop, moving in a gently upward path described by a quadratic curve.
Example 3: A football player kicks the ball upward, which follows a quadratic path as it travels a distance.
