If I can run 1/4 mile in 3 minutes how long would it take me to run 26.2 miles?
1 answer:
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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
The answer is: 12 centimeters.
The explanation is shown below:
1. By definition, all four sides of the square are equal and the diagonals are equal too.
2. Keeping the information above on mind, you know that AC and BD are equal:
3. Then, the length of BD is twice BE. So, you can calculate it as following:
4. Therefore, the lenght of AC is: