future

1)Agricultural Engineering
From what I researched agricultural engineering is basically designing and making agricultural tools, plants, and machinery . the demand for agricultural engineers is supposed to increase within the next years because of global warming and other factors. It pays a decent salary around 40,000 to 70,000.

2)Civil Engineering
Civil engineers make and come up with big projects and buildings such as the white house, pentagon, many buildings. They design, plan, and run large building projects, such as bridges, buildings, roads, dams, and water-supply systems. Basically any big projects, they find ways to build. Its said that it will increase in the next years and the salary is around 80,000.

3) Aircraft and Avionics technicians
what they do is basically inspect airplanes and helicopters whether they have a defect or are deteriorating or wearing down and fixing or repairing them. The outlook for it s good, it will increase average. The normal salary would be around 50,000, but it includes some benefits like getting ur ticket cheaper .

the main universities that I would go to would be UCLA,USC, basically and UC but it doesn’t hurt trying other universities.

1)UC Davis: has major in civil engineering,percentage acceptance is 53%, and it doesn’t look to be that bad, 58% had a GPA of 3.75, almost there, just one point behind, so I should pass that.

2)Kansas state university: has a major for air crafts mechanics.80% acceptance rate. Its in Kansas, which most are white and Hispanics are a minority

3)Auburn: has an acceptance rate of 73 and has major in agricultural engineering. Its in a large town, more women than men, Hispanics are a minority, 2%. seems like a decent university.

transformationnnsss

1)The way I remember transformations is that for example in this function 2cos(4x+1)+2. the 2 would be basically the limit of how far the line can go vertically, in this case it would be two or where the line would start off touching. The 4 would be how much it horizontally shrinks or stretches; in this case it would shrink. The 1 would make it shift horizontally to the left on the x-axis since it is in parenthesis with the input. The 2 would make the output shift to the left 2 because since its plus, and you do the opposite if the 2 was minus 2, then u would do the opposite of that and shift it to the right side 2 units. If there is a negative sign in front of the 2 or cos when there is not a number in front of it, then the function or line flips.

2)It’s pretty easy to memorize the unit circle. Think about it like this. You start at 0, which is (1,0). Then just memorize that it is 3,2,1 for the first quadrant, for the second quadrant, at pie/2, its (0,1), then its 1,2,3, then its pie and its (-1,0) then its 3,2,1, then its 3 pie/2, (0, -1) then its 1,2,3. Then just fill out the rest, for 3, its square root of 3/2, for 2 its square root of 2/2, and for 1 its ½. This is an easy way to remember cos, you would just have to remember sin and it would be easy. Just remember also where the negative go and it will be easy.

3)What worries me or what I do not understand completely is finding the domain of some of the graphs, is there an easier way to memorize or to do the domain and range?

logs and inverses

to determine whether a function is one to one you can use the horizontal line test. when you use the horizontal line test, if there is more than one point on the horizontal line, then it is not one to one.

to find the inverse of a function, after graphing the function, you can switch the table of values so that what used to be x is now y and what used to be y is now x and what used to be the domain for the graph now becomes the range and what used to be the range becomes the domain. Basically you switch x and y.

whenever you have to solve an equation algebraically such as in an equation like (1.045)^t= 2,you would take the natural log or Ln of both sides and try to solve for t or x or any unknown. in this case after putting Ln on both sides,u would divide Ln 2 by Ln 1.045 and you would get what t equals.

whenever something has the base of e or the base of Ln, in order to get x or an unknown alone and u want to solve it, in the case of e, u would take the Ln of it and it would cancel and what ever you do to one side u would to to the other side and u would solve it. for example if its e^0.05t=3, u would Ln both sides lne^0.05t= Ln3 and after u solve it it would equal t = about 21.97 but if it had the base of Ln, then u would add the base of e to both sides and solve it


what i don't understand is when do we use log, is it only when something has the base of log or i don't know,. i also do not understand how to solve for two X's, such as in this equation 2^x + 2^-x =5. i also do not get how to prove f is its own inverse, such as in number 45 on page 44 and finding formulas for f-1 on page 44 numbers 43 and 44. i also don't really understand what solving an equation algebraically really mean, i just know what to do.

even and odd functions

Even functions

whatever the input is, whether its positive or negative, if the output comes out positive then the function is even, but if it comes out negative its an odd function. For example in the function of f(-x)= x^2, if you plug in a negative number such as -1, it comes out positive, f(-1)=(-1)^2 , f(-1) = 1 , if one were to graph it, it would be symmetrical about the y axis, the only number that would change would be the x, if it was 2 in the x axis in quadrant 1, then in quadrant 2 the x would be -2, but the y would be the same for both quadrants. In other words, what ever the input is, if the output is positive, then the function is even and symmetrical to the y-axis.

odd function

an example of a odd function would be f(-x)=x^3. If x were to be -1 like this, f(-1)= (-1)^3, it would equal f(-1)= -1, it would be negative. In this case, it would be symmetrical about the origin meaning that it would look the same if one of the sides was flipped either upside down or right way up. But since it is not symmetrical about the y-axis, it is symmetrical about the origin, across from each other, like in the graph, one side is in quadrant one while the other is in quadrant three. In other words, what ever the input is, if it comes out negative, then the function is odd and is symmetrical about the origin.