Math 11 – Ruben's Blog

week 17 – precalc 11

rubeng2016 on January 14, 2019January 14, 2019

this week I math we learned to how to use Sin law to find either a certain angle of a triangle or a side length. In order to use Sin law you at least three clues, of those three clues you need to have an angle and the corresponding side length of that angle.

below is a triangle that you would be able to use Sin law with

The angle of “C” is not directly given however, you can determine the angle subtracting the other two angles from 180 as all angles in a triangle have to add to $180\textdegree$

you now know that angle C is $63\textdegree$ . With this information, you can find either side a or side b with the formula $\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{b}{sin75}=\frac{22}{sin63}$

$b=\frac{22(sin75)}{sin63}$

$b=24cm$

week 15- precalc

rubeng2016 on December 16, 2018

This week in math we learned how to simplify an expression when they are adding.

$\frac{6}{a-3}+\frac{2}{a+7}$

The non-permissible values are A cannot equal 3,-7. The next step is to multiply both fractions by a common denominator

$\frac {6 \times (a+7)}{(a-3)\times (a+7)}+\frac{2\times(a-3)}{a+7\times(a-3)}$

$\frac{6a+42+2a-6}{(a-3)(a+7)}$

then collect like terms

$\frac{8a+36}{(a-3)(a+7)}$ is what you are left with

week 14 – Precalc

rubeng2016 on December 16, 2018

This week in math we learned how to simplify a rational expression and determine the non-permissible values. The expression below is an example of how to do this.

$\frac {10y}{(y-3)^3}\div{\frac {y(y+1)}{(y-3)^2}}$

The first step is to determine the non-permissible values which for now are only Y cannot equal 3.

$\frac {10y}{(y-3)(y-3)(y-3)}\times{\frac {(y-3)(y-3)}{y(y+1)}}$

Now that you have flipped the fraction you have to determine the new non-permissible values of the second fraction which are, Y cannot equal 0,-1.

you can now cross out the top of the fraction with the bottom of the fraction. Then you end up with:

$\frac {10}{(y-3)(y+1)}$

Week 13 – precalc

rubeng2016 on November 30, 2018

This week in math we learned how to graph the reciprocal of a quadratic function. Below will be an example of how to do this:

$y=-3x^2+9$

the first step is to graph the parent function which would look like this.

By looking at the graph you can determine a couple of things.

asymptotes: X= 1.7, x=-1.7 y=0

invariant point (1.6,1)(-1.6,1)(-1.8,-1)(1.8,1)

This gives you all the information that you need to graph the equation once you reciprocate it

the reciprocated function should look like this $y=\frac{1}{-3x^2+9}$

the hyperbola above the x-axis is located at the reciprocal of the vertex which in this case is $\frac{1}{9}$

The end result should look like this.

Week 12 -precalc

rubeng2016 on November 27, 2018

This week in math we learned how to determine the points of intersection of a linear absolute value equation, for example

:|2x-3|=9

the first is to split the equation into separate ones. one of them you have to replace the absolute value signs with brackets then place a negative in front that has to be distributed followed by solving as shown below.

-(2x-3)=9

-2x+3=9

-2x=6

x=-3

The second step is to just remove the absolute value signs from the equation then solve

2x-3=9

2x=12

x=6

you can now determine that for the two points of intersection x would equal x=-3 and x=6

Week 11- Precalc

rubeng2016 on November 21, 2018

this week in math we learned how to determine the points of intersection with a linear and quadratic system

the two systems that are going to be used are

$y=-2x^2+8$

and

$3x-y=-3$

First, you have to graph the quadratic which should not be that difficult since it is already in vertex form

the next step is to graph the linear system which involves a few more steps

first you must rearrange the system so that the Y is isolated and positive. After you rearrange the linear function it should look like this

$y=3x+3$

from this, you can determine that the y-intercept is 3 and that it has a positive slope of 3. you now should have all the information to graph it.

from this point, you simply follow the course of both functions to find where they intersect with one another

in this case the there were two points that intersected, they were (1,6) and (-2.5,-4.5)

Week 10 – Precalc

rubeng2016 on November 19, 2018

This week we learned how to solve a quadratic inequality.

example: $x^2-x-12\leqslant{0}$

The first step would be to rearrange the inequality but in this case, it is not necessary.

so you would the factor the equation

$(x-4)(x+3)$

$x=4 x=-3$

The next step is to choose a number to use as a test point to determine which section of the graph satisfies the inequality

$(-4)^2-(-4)-12\leqslant{0}$

$16+4-12\leqslant{0}$

$8\leqslant{0}$

This is not true so it does not satisfy the inequality

Then test another point between -3 and 4, 0 will be the number that is used

$0^2-0-12\leqslant{0}$

$-12\leqslant{0}$

this is true so it satisfies the inequality

lastly, you have to test a point that is greater than or equal to 4, we will use 5

$5^2-5-12\leqslant{0}$

$8\leqslant{0}$

this is not true therefore it does not satisfy the inequality. This means that the only solution is $-3\leqslant{x}\leqslant{4}$

week 9- precalc 11

rubeng2016 on November 5, 2018

This week in math we learned how to solve a word problem for quadratic functions. The following is an example:

A TV company sells TVs for $400. At that price, they can sell 500 per week, the company predicts that for every $50 increase in price, they will sell 20 fewer TVs. what price for a TV will maximize the revenue?

The first step is come up with figure out what formula to use based on the vocabulary used in this case you would use the formula to figure out revenue

Revenue=(price)(#of sales)

$R=(400+50x)(500-20x)$

The next step is to foil this equation

$R=-1000x^2+17000+200,000$

Next, you have to get the function to vertex form by completing the square

$R=-1000(x^2-17+\frac{289}{4}-\frac{289}{4})+200,000$

Then factor and add

$R=-1000(x-\frac{17}{2})^2+272,250$

Vertex:(8.5,272,250)

Now you know that to maxamize revenue they can increase the price 8.5 times for and increase in profit of $72,250

Week 7 Precalc

rubeng2016 on October 25, 2018November 2, 2018

In math, we learned how to solve a quadratic equation using the quadratic formula

$x=\frac {-(b)\pm \sqrt {(b)^2-4(a)(c)}}{2a}$

This method of solving will be used to solve the equation:

$(2x+1)^2+4=49$

before you can use the formula you first have to expand and make the right side of the equation equal zero

$(2x+1)(2x+1)+4-49=0$

Then foil and collect like terms

$4x^2+2x+2x+1-45=0$

$4x^2+4x+1-45=0$

$4x^2+4x-44=0$

from this point, you can look for a common factor to take out in order to make the equation easier. in this case, the common factor is four

$x^2+x-11=0$

Now you are able to use the quadratic formula to solve

A=1

B=1

C=-11

$x=\frac{-(1)\pm \sqrt{(1)^2-4(1)(-11)}}{2}$

$x=\frac{-1\pm \sqrt{1+44}}{2}$

$x=\frac{-1\pm \sqrt{45}}{2}$

$x=\frac{-1\pm 3\sqrt{5}}{2}$

Week 8- precalc 11

rubeng2016 on October 25, 2018November 1, 2018

This week in pre-cal we learned how to read an equation and determine the vertical and horizontal translations, and also how to determine whether it is a stretch, compression and/or a reflection

In the function $y=-4(x+3)+5$

you can determine that the vertex is (-3,5), that is is a stretch and a reflection over the x-axis, and that the stretch is congruent to 4,12,20. the line of symmetry is -3

this was vertex is determined by the 3 and the 5 in the function above, the sign in front of the number in the brackets is the opposite to find the vertex. You determine whether or not it is a reflection by the coefficient in front of the brackets. If the coefficient is negative then it is a reflection, if it is positive it opens up. the stretch is determined by the coefficient as well if it is a whole number the parabola narrows as the number gets bigger. if the number is less than one the parabola compresses

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