Answer:
r = 144 units
Step-by-step explanation:
The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;
In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.
Substituting the terms of the equation and the derivative of r´, as follows,
Doing the operations inside of the brackets the derivatives are:
1 ) 
2) 
Entering these values of the integral is
It is possible to factorize the quadratic function and the integral can reduced as,
Thus, evaluate from 0 to 16
The value is 
(8/9-3/9)*2/3=5/9*2/3=10/27
Answer:
The inductive reasoning is based on A: a limited number of observations
Step-by-step explanation:
Let's say you lived until 90 years old, and took a observation on July 4th each year. Even if you lived until 90 years old, you would only have 90 observations. And inductive reasoning allows for statements to be false, so any of the 90 observations that you took can be proven false. So really, you would have only 90 observations, with any of them that could be false. A limited number of observations would be the only thing that you could base this reasoning off of.
162.15 is the answer because you have to multiply 0.15•141 then add 21.15 to the 141 :)
Answer:
n=4
Step-by-step explanation:
Given equation: \[\frac{1}{n-4}-\frac{2}{n}=\frac{3}{4-n}\]
Simplifying the Left Hand Side of the equation by taking the LCM of the denominator terms:
\[\frac{n}{n*(n-4)}-\frac{2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{n - 2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{n - 2n + 8}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{8 - n}{n*(n-4)}=\frac{3}{4-n}\]
=> \[(8-n)*(4-n) =n*(n-4)*3\]
=> \[n-8 =3n\]
=> \[2n =8\]
=> n = 4
