Week 17-Precalculos 11

This week you learn how two laws, cosine law and sine law.

For you to differentiate the two laws and to get the exercise, you have to know that the cosine law you need to have two sides and one angle. And for the sine law you need two sides and one side. But you need to understand the exercise, sometimes he can ask the angle and sometimes the side, and for each one you have a different formula.

THIS IS SINE.

Resultado de imagem para fórmula da lei de seno pra lados e ângulos
THIS IS COSINE.
Resultado de imagem para cosine law

Week 16-Precalculos 11

So, this week we learned about trigonometry. You have to decorate the Soh Cah Toa that will become easier. We have the cosine, seni and tangent. For each of them we have a fraction, the cosine is adjacent under hypotenuse, the sine is opposed under hypotenuse and the tangent is opposite under adjacent.

And each of them has its angles and formulas.

Week 15-Precalculos11

OK, this week I learn about Application of Rational Equation is like a problems.

In most you will have and will be able to divide over the distance the speed and the time.  Well, you will have a paragraph with numbers and key words, and with that you will have to assemble an equation and solve.

The most difficult part is to assemble the equation, you need to read several times and circulate the key words like less or more, distance, from, then, km these things, will help you. The distance by the time the time by the speed and so it goes.

Example:

A natural number is 4 MORE than another natural number. When the RECIPROCAL  of the GREATER number is subtraced FROM the reciproral of the LESSER number, the difference is 1 over 15. What are the two numbers?

  1. read two times
  2. circle the key words, like the ones in capital letters.
  3. more is like +, less is – and from you have to change the equations places.

 

 

 

 

Week 14-Precalculos 11

This week we learn about Racional Expressions, basically is with fractions and we can add, subtract, multiply and divide. I will give examples that each:

Add: You first need to see the number you can divide by it, such as 2, 4, and 6, the minimum common multiplier is 12 because 2×6 = 12, 4×3 = 12, 6×2 = 12, and then you’re just the numerators.

Subtract: You need to do the same thing, but instead of adding you subtract.

Multiply: In multiplication you only have to multiply the numerators by the numerators and denominators by the denominated ones and you can have a chance such as 18 over 8 and multiplied by 2 over 9, you cut the 18 with the 9 by itself and the 2 and 8 by it even, the result would be 2 out of 4.

Divide: You do the same only in the second fraction you reverse the numerators down and the denominators up and then there is a multiplication and so is the same process.

Add:

Imagem relacionada

Subtract:
 Resultado de imagem para fotos de subtracao de fracao
Multiple:
Resultado de imagem para multiple fractions
Divide:
Resultado de imagem para multiple and divide fractions

 

Week 13- Precalculos 11

This week we learn about Reciprocal Functions.

First we need a equation like -3x+ 2 because with this line we can find the invariant points that is y= 1 and y= -1 and after we need put a line between these two points on vertical and the horizontal line, for last one we graph.

This is example the Reciprocal Linear, to know that it is linear is just take the two points and see if a line or a parabola.

This example is Reciprocal Quadratic, to know if it is quadratic is the same only if we get the points and if you make a parabola is quadratic.

 

Week 12- Precalculos 11

This week I will talk about systems, which is when we have two equations and we can use elimination, substitution or addition. I’ll give some examples :

x-2y= -10 and 3x-y= 0 , to substitution we have x=2y-10 and with this 3(2y-10) – y =0  so we do the distribution, 6y- 30 – y=0 then 5y- 30= 0 and 30 divided by 5 is y=6

The same equation For elimination :

-3x + 6y= 30 less 3x-y = 0 we have 5y=30 and y=6, by elimination was easier because we only have to put one equation below the other and multiply by a number to be subtracted and the result is zero.

 

Week 11- Precalculos 11

This week we learned solving quadratic systems.

This graph is an example that we have only one solution because the two lines intersect at only one point: Resultado de imagem para exemplos de solving quadratic systems with one solution

This we have infinity points because one on top of the other so they intersect at the same point:

Imagem relacionada

And then we have what has no solution, because the lines do not intersect at the same point:

Resultado de imagem para solving equations infinite systems

 

Week 10- Precalculos11

This week we learn about Solving Quadratic, to find the points and then put in the graph we can solve by factoring and then put in a line that in the middle is the 0.

If you give to me 0>– 2x, the two points will be x = 0 and x = 2 and placing on the line the zero will be in the middle and the two to the right because it is positive.

Another example is  + 2x- 8 > 0 and then y=  + 2x -8  after with the factoring we have y=(x+4)(x-2), x=-4 and x=2 and now we have the points. Lastly we need see with the solution is true or false.

Week 9- Precalculos 11

Modelling problems

When in a problem they put SUM you must know that it is speaking of sum and when it appears PRODUCT is speaking of multiplication. And

  • l (length),
  • w (width)
  • h (height)

Easy example= on our street there are twice as many dogs as cats. How do we write this as an equation?

  • Let D = number of dogs
  • Let C = number of cats

 D = 2c

Week 8-Precalculos 11

When it gives you a graph, you need to know how to find the Damain, Range, x-intercept, y-intercept, and the symmetry line and whether it is linear.

  1. b2 – 4ac < 0 and the parabola has no x-intercepts.
  2. b2 – 4ac = 0 and the parabola has exactly one x-intercept.
  3. b2 – 4ac > 0 and the parabola has two x-intercepts.

Examples =

Graph of Quadratic Function Graph of Quadratic Function Graph of Quadratic Function Graph of Quadratic Function Graph of Quadratic Function Graph of Quadratic Function