Please use the newton Cotes formulas for intergration. In addition all coding parts should be done in PYTHON. trinket.io is a nice free python coding platform

In the design of a new high performance Olympic pool, you are hired as computational expert The contractor is very interested in the control of various indicators (temperature, PH, and Cl concentration). A recent study of the Australian Federation has revealed that these parameters can affect dramatically the performance of the swimmers. For this reason, an automated system has to be installed in order to keep track of these measures. The dimensions of the pool are 50x25x3 m The first approach is to place eight multisensors at the 8 corners (0; 0; 0), (50; 0; 0), (50; 25; 0), (0; 25; 0), (0; 0; 3), (50; 0; 3), (50; 25; 3) and (0; 25; 3) (a) The first values of interest are the averages for temperature, PH, and Cl concentration. Write the analytical expression (integral) for computing these averages. Propose and write the expression for a quadrature that is adequate with the current position of the sensors. To which quadrature corresponds your proposal and why? Generate a random vector of values for the 8 sensors, and write the code to compute the correspondent averages (b) Some studies point that there could be a thermal stratification phenomenon: the temperature is almost constant at a particular depth, but varies quadratically in this depth direction (z). If we want to be accurate in our integration, are the sensors in a good position now? If yes, justify If not, propose an optimal distribution of sensors (minimum necessary, indicate number and coordinates) and a correspondent quadrature. Write the code for this quadrature and perform the average using a vector that resembles a quadratic distribution of temperature in depth c) For unknown reasons, the Cl concentration presents a cubic variation in the three dimensions, with high spikes on the corners, so those points should be included in the computation. Is the sensor distribution enough to have a good accuracy now? If not, propose an optimal distribution of sensors (minimum necessary, indicate number and coordinates) and a correspondent quadra- ture. Write the code for this quadrature and perform the average, using a cubic distribution in your data vector, and increasing a 20% the values initially obtained in the corners. d A budget cut motivates the switch from a very accurate sensing device to a not so reliable one, but very cheap. The error can be considerable, so its preferable to place many of them along every direction and use a combined quadrature, in which every zone between the sensors is treated with a trapezoidal rule. Write the code to perform this combined quadrature to compute this average using a n+1 number of cheap sensors. For the data, use a quadratic distribution in each direction, and then apply a random 10% to the resulting vector. Comment on the error as we increase n In the design of a new high performance Olympic pool, you are hired as computational expert The contractor is very interested in the control of various indicators (temperature, PH, and Cl concentration). A recent study of the Australian Federation has revealed that these parameters can affect dramatically the performance of the swimmers. For this reason, an automated system has to be installed in order to keep track of these measures. The dimensions of the pool are 50x25x3 m The first approach is to place eight multisensors at the 8 corners (0; 0; 0), (50; 0; 0), (50; 25; 0), (0; 25; 0), (0; 0; 3), (50; 0; 3), (50; 25; 3) and (0; 25; 3) (a) The first values of interest are the averages for temperature, PH, and Cl concentration. Write the analytical expression (integral) for computing these averages. Propose and write the expression for a quadrature that is adequate with the current position of the sensors. To which quadrature corresponds your proposal and why? Generate a random vector of values for the 8 sensors, and write the code to compute the correspondent averages (b) Some studies point that there could be a thermal stratification phenomenon: the temperature is almost constant at a particular depth, but varies quadratically in this depth direction (z). If we want to be accurate in our integration, are the sensors in a good position now? If yes, justify If not, propose an optimal distribution of sensors (minimum necessary, indicate number and coordinates) and a correspondent quadrature. Write the code for this quadrature and perform the average using a vector that resembles a quadratic distribution of temperature in depth c) For unknown reasons, the Cl concentration presents a cubic variation in the three dimensions, with high spikes on the corners, so those points should be included in the computation. Is the sensor distribution enough to have a good accuracy now? If not, propose an optimal distribution of sensors (minimum necessary, indicate number and coordinates) and a correspondent quadra- ture. Write the code for this quadrature and perform the average, using a cubic distribution in your data vector, and increasing a 20% the values initially obtained in the corners. d A budget cut motivates the switch from a very accurate sensing device to a not so reliable one, but very cheap. The error can be considerable, so its preferable to place many of them along every direction and use a combined quadrature, in which every zone between the sensors is treated with a trapezoidal rule. Write the code to perform this combined quadrature to compute this average using a n+1 number of cheap sensors. For the data, use a quadratic distribution in each direction, and then apply a random 10% to the resulting vector. Comment on the error as we increase n