Chapter 9.49, Problem 49.7E

The accompanying data shows the fossil fuels​ production, fossil fuels​ consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year    Fossil Fuels Production    Fossil Fuels Consumption    Total Energy Consumption1949    28.748    29.002    31.9821950    32.563    31.632    34.6161951    35.792    34.008    36.9741952    34.977    33.800    36.7481953    35.349    34.826    37.6641954    33.764    33.877    36.6391955    37.364    37.410    40.2081956    39.771    38.888    41.7541957    40.133    38.926    41.7871958    37.216    38.717    41.6451959    39.045    40.550    43.4661960    39.869    42.137    45.0861961    40.307    42.758    45.7381962    41.732    44.681    47.8261963    44.037    46.509    49.6441964    45.789    48.543    51.8151965    47.235    50.577    54.0151966    50.035    53.514    57.0141967    52.597    55.127    58.9051968    54.306    58.502    62.4151969    56.286…

For each of the time​ series, construct a line chart of the data and identify the characteristics of the time series​ (that is,​ random, stationary,​ trend, seasonal, or​ cyclical). Month    PercentApr 1972    4.97May 1972    5.00Jun 1972    5.04Jul 1972    5.25Aug 1972    5.27Sep 1972    5.50Oct 1972    5.73Nov 1972    5.75Dec 1972    5.79Jan 1973    6.00Feb 1973    6.02Mar 1973    6.30Apr 1973    6.61May 1973    7.01Jun 1973    7.49Jul 1973    8.30Aug 1973    9.23Sep 1973    9.86Oct 1973    9.94Nov 1973    9.75Dec 1973    9.75Jan 1974    9.73Feb 1974    9.21Mar 1974    8.85Apr 1974    10.02May 1974    11.25Jun 1974    11.54Jul 1974    11.97Aug 1974    12.00Sep 1974    12.00Oct 1974    11.68Nov 1974    10.83Dec 1974    10.50Jan 1975    10.05Feb 1975    8.96Mar 1975    7.93Apr 1975    7.50May 1975    7.40Jun 1975    7.07Jul 1975    7.15Aug 1975    7.66Sep 1975    7.88Oct 1975    7.96Nov 1975    7.53Dec 1975    7.26Jan 1976    7.00Feb 1976    6.75Mar 1976    6.75Apr 1976    6.75May 1976…

Using FDF, BDF, and CDF, find the first derivative; 1. The distance x of a runner from a fixed point is measured (in meters) at an interval of half a second. The data obtained is: t 0 x 0 0.5 3.65 1.0 1.5 2.0 6.80 9.90 12.15 Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s 2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input of 2 assuming a step size of 1. Calculate using Analytical Solution and Absolute Relative Error: = True Value - Approximate Value| x100 True Value 3. Given the data below where f(x) sin (3x), estimate f(1.5) using Langrage Interpolation. x 1 1.3 1.6 1.9 2.2 f(x) 0.14 -0.69 -0.99 -0.55 0.31 4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given by: 30 x = Loo (2000ln 140000 140000 - 2100 9.8t) dt Using the Trapezoidal Rule, n=2, find the distance covered. 5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the results for n=4 and n=8

Can you check if my step is correct?

I need help explaining on this example on how can I define the Time-Domain Function, Apply the Laplace Transformation Formula, and Simplify to Find the Frequency-Domain Expression. I need to understand on finding Y(s)

1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b) the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the 8-second period. t 0 2 4 6 8 V 10 15 12 10 16 2. Find the midpoint rule approximation for (a) n = 4 +5 x²dx using n subintervals. 1° 2 (b) n = 8 36 32 28 36 32 28 24 24 20 20 16 16 12 8- 4 1 2 3 4 5 6 12 8 4 1 2 3 4 5 6

1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat over one period may be approximated by the function, f(x) = 0.005x4 2 0.005x³-0.364x² + 1.27x on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from that used in any other posts on this topic, to generate a periodic function that can be used to model its heartbeat, and graph your result. Be sure to include your chosen value of n in your Subject Heading.

I need help explaining on this example on how can I define the Time-Domain Function, Apply the Laplace Transformation Formula, and

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