Gradient Functions
In the following coursework, will investigate the gradient functions
using the formula y=ax^n, where a is a constant and n is a number.
a
n
Y=ax^n
1
1
x
2
1
2x
3
1
3x
4
1
4x
5
1
5x
a
n
Y=ax^n
1
2
x
2
2
4x
3
2
6x
4
2
8x
5
2
10x
a
n
Y=ax^n
1
3
3x^2
2
3
6x^2
3
3
9x^2
4
3
12x^2
5
3
15x^2
a
n
Y=ax^n
1
4
4x^3
2
4
8x^3
3
4
12x^3
4
4
16x^3
5
4
20x^3
I will plot the graphs of the functions above and I will find their
gradient using the formula gradient=increase in y-axis /increase in
x-axis.
Straight line graphs
Straight line graphs are graphs with the equation y=mx+c or y=ax^1,where
is stand for the gradient and c is the y- intercept.
Gradient calculations
1. y=x graph
Gradient of A= increase in y -axis/increase in x-axis
= 2/2
=1
Gradient of B= increase in y-axis/increase in x-axis
= 2/2
=1
2. y=2x graph
Gradient of D= increase in y-axis/increase in x-axis
= 4/2
=2
Gradient of E= increase in y-axis/increase in x-axis
= 4/2
=2
Gradient of F= increase in y-axis/increase in x-axis
Our predicted points for our data are, (13, -88.57) and (-2, -29.84). These points show the
For my derivative project I chose to graph Emmitt Smith’s annual rushing yard total. Emmitt was drafted out of University Florida in 1990 and began his career as an NFL Great. As you can see on the graph, Smith began his career slowly, amassing only 937 rushing yards his rookie year. However, his second year Smith improved to 1563 rushing yards. In his third season, Smith again improved to 1713 rushing yards. The decrease in production Smith’s fourth and fifth year (1486 and 1494 respectively) in the NFL can be partially credited to the fact Smith did not compete in all sixteen regular season games due to injuries. Smith redeemed himself the following year with a career high 1773 rushing yards. Over the next six years Smith’s age slowly caught up to him as he ranged from 1021 to 1397 yards. Finally, after his thirteenth year as a Dallas Cowboy, Smith was traded to the Arizona Cardinals. In his first year with the Arizona Cardinals (2003), Smith was injured and played as a backup for the majority of the year. This is illustrated through his career low 256 rushing yards. However, in Smith’s final year in the NFL, he rushed for 937 rushing yards, bouncing back from a disappointing year. Strangely, Smith ended his last season with the same rushing total as his rookie season. I plotted these points in a graph in an excel document and created a line of best fit. This line was a cubic equation (f(x) = 1.4228x3 - 8533.3x2 + 2E+07x - 1E+10).
This equation shifts from the parent function based on the equation f(x) = k+a(x-h) . In this equation, k shifts the parent function vertically, up or down, depending on the value of k. The h value shifts the parent function to the left or right. If h equals 1, it goes to the right 1 unit, if it is negative 1, it goes to the left 1 unit. If a is negative, the parent function is reflected on the x-axis. If x is negative, the parent function is reflected on the y-axis.
Derivatives as defined by Warren Buffet are time bombs, both for the companies that make use of them and the monetary framework. Fundamentally these instruments call for cash to change hands at a future date, with the add up to be dictated by one or more reference things, for example, premium rates, stock costs, or money values. Case in point, in the event that you are either long or short a S&P 500 prospects contract, you are a gathering to an extremely straightforward derivatives transaction, with your addition or misfortune determined from developments in the list. Derivatives contracts are of shifting length of time, running now and again to 20 or more years, and their quality is regularly attached to a few Variables.
On Thursday, September 17th, 2015 at approximately 1845 hours while working as a Loss Prevention Agent for Nordstrom store 626, located in Annapolis, Maryland, I, Michael Hugg observed via CCTV (Closed Circuit Television) an unknown male later identified as David James Jackson Jr. enter the Rail department. I began observation of Jackson due to the quick selection of one black Howe ‘White lie’ jacket followed by furtive eye movement.
Kenneth Pomeranz‘s The Great Divergence tries to examine the classic question of ‘How do we account for the economic divergence between Europe and Asia? He acknowledged that ‘a surge in European technological inventiveness was a necessary condition of the Industrial Revolution’, but stressed on the crucial role of ‘coal and colonies’ and their critical geographic location, in lifting the constraints for sustained growth of per capita income. First the local coal deposits in Europe were closer to the cities than in China and this gave Europe a clear advantage. Second, the off-shore colonies, in particular, the closeness of Europe to the New World resources (Jones 1981, Wrigley 1988, Allen 2009) helped Europeans to overcome the difficulties
According to IBISWorld, the department store industry faces high levels of competition. Therefore, it is essential for stores such as Nordstrom to distinguish themselves from other retailers. As of 2014, Nordstrom operated more than 117 full-line stores, 142 off-price Nordstrom rack stores, and an online store, which earned the company a profit of $1,350 million according to EBSCOhost. This high-end department store attracts customers by utilizing positioning strategies involving product assortment, store experience, prices, and retail technology.
The Earth’s surface is ever changing, and each region has different rates of change (Westaway, 2017). This is completed through lateral transport processes such as water, wind and mass movement, while ice is one too it doesn’t apply in Australia. Mass movement happens on sloping ground where huge slabs of the ground surface detach and slide or flow downhill (Government of South Australia, 2016). It occurs in Australia due to the extreme wetness causing the soil to be weak and gain mass, or by earthworks such as track cutting. Slope plays a key role in mass movement and virtually any slope steeper that 30% is at risk. South Australia is home to permeable substrate materials, shale, bedrock and depending on
Analysts will input the following information into a simple linear regression model provided in Excel QM using a simple linear regression formula Yi =b_0+ b_1 X_1. In FIGURE 1-3 the highlighted Coefficients are provided. The b_0 is -18.3975 and the b_1 is 26.3479, these coefficients are added to the formula that is represented in figure 1-4.
gradient of this graph = - (Ea / RT) which can be used to calculate
The curvilinear relationship amongst age and crime is a standout amongst the most steady discoveries in criminology, and it has been alluded to as a “resilient empirical regularity” (Brame & Piquero, 2003, p. 107. Social analysts as right on time as Quetelet in the 1800s (Steffensmeier, Allan, Harer, and Streifel, 1989) recognized a solid relationship amongst age and crime that has come to be known as the age–crime bend. The general type of the relationship amongst age and crime is very little bantered about. In total reviews, the age–crime bend is unimodal, with authority crime rates ascending in youth to a crest in the late young years and after that declining quickly through adulthood. It is likewise evident that the age–crime bend crests
method can be produced and a graph of the function can be made. From the graph,
Classification of Derivatives: Derivatives are classified in terms of their payoffs and as exchange traded and over the counters.
The dates regarding the advent of Mathematical Physics vary just as how the dates concerning the advent of Mathematics and Physics vary from person to person and from tale to tale. There is an account which says that the methods of Mathematical Physics as a theory of mathematical model in Physics can be traced in the works of Newton and his contemporaries such as Lagrange, Euler, Laplace, Gauss and others who contributed in the advancement of methods of Mathematical Physics. However, there is a version especially that of which written in The Evolution of Mathematical Physics (1924) by Lamb laying the mark of its birth in 1807; the date after the French Revolution had subsided and later succeeded by the relative tranquility of the early empire, and the year when Laplace, Lagrange, and several other mathematicians used Newton’s scientific work to model, describe and predict the motion of celestial and terrestrial bodies. In this age, the methods of Mathematical Physics were successfully used in studying mathematical models of physical phenomena. These models have something to do with electrodynamics, acoustics, theory of elasticity, hydrodynamics, aerodynamics, and other related areas. The models used were usually described using partial differential equation, integral and integrodifferential equations, variational and probability theory methods, potential theory, the theory of functions of complex variable. Some of the dominant western mathematicians and scientist who succeeded in studying and describing the physical world by mathematical modeling are Lord Kelvin, George Stokes, James Clerk Maxwell, and Guthrie Tait.
Optimization is a chronic and natural process usually witnessed in our daily life events. In various disciplines such as engineering designs, manufacturing systems, agricultural sciences, physical sciences, economics, pattern recognition etc. optimization is observed. Optimization is, thus a process of making best, effective and functional solution out of possible choices no way differs from the structural optimization which is being conceived in the present work. Structural optimization is a decisive and tricky step, where the designers are able to generate better designs saving time and money. Conventional optimization approaches like mathematical programming method, optimality criteria method etc. fails miserably in structural design problems which are highly complex and time consuming in nature. Optimization problems are mathematical models formulated to solve complex designs that may be of multi-objective nature in certain cases. Structural design procedure involves conceptual design and design realization leading to several probable results since higher degree of ambiguity is experienced in every steps. Conceptual design phase is more dependent on decision variables than in advance optimization phase. Optimization is one of the major tool for decision making at the conceptual or realization phase of modern design techniques. In design realization stage optimization is achieved by mathematical and numerical search methods.