like my last post this is a method of multiplying but not just binomials I just used binomials to example this expression
this is an easier way to multiply binomials because you can really see it here where the 6x and the 5x add together, it’s basically like a multiplication table where you just fill in the boxes and do the equation
This method of multiplying binomials is called the claw or FOIL which stands for front, inside, outside, and last
It’s one of the more simpler ways to multiply binomials and what you do is take the first two numbers or variables in this case and you multiply and with this question it equals X squared than we take it to the outside and inside which are most likely going to be like terms and with this question it was, it was 6x and 5x and since they’re both positive they equal 11x, to simplify that you basically just add them when it’s all positive and then finally you multiply the final two to give you 30
This here are the three equations possible with sine, cosine, and tangent as well as the three places you could have a variable and you need to find out what the variable is.
for the first equation you have a tangent equation and they’ve already given you the opposite and adjacent and now you have to find out what the variable equals so you have to turn to inverse tangent and divide the opposite over adjacent then multiply inverse tangent with the division you just did. For the cosine equation you have the reference angle and the hypotenuse and they’re asking you to find the adjacent side so what you do is take the reference angle and multiply it with cosine then multiply that with the hypotenuse which should give you the adjacent side. for the third you have a sine equations and they’ve given you the reference angle and the opposite side and the variable is in place of the hypotenuse so what they want you to do is take the opposite side and divide it with sine times 23 which should give you the hypotenuse and you have to always make sure your results make sense and to not concentrate on your illustration of the triangle but only on the information given to you
calculating a sphere versus a hemi-sphere is basically taking a sphere and cutting the calculations in half
for volume you literally take the calculations as you can see from 4/3 there and you cut it in half and you have 4/6 for the hemi-sphere. For surface area it’s not exactly half you just take one off the 4
the volume of a cone is exactly 3 time a cylinders and it is simply a formula.
first thing you do is you have to know the formula that you’re using so I have mine already in place ready for me to input my numbers so after you input the numbers what I did is square the radius, multiply the squared radius with the height, multiply that with Pi, and finally divide that with 3 to get your cone from the cylinder
the negative exponent law is basically taking a negative exponent and turning it into a positive exponent so that it is easier to work with.
the way Ms. Burton taught us to do it is to make it into a fraction like the image above and to think of it as upstairs and downstairs if an exponent doesn’t like it on a certain floor then it is negative so to get it positive you have to make it happy and move to the only other floor (refer to example in the image)
the zero exponent law is basically a law that tells you that whichever number and it can be any number to the power of zero equals
it equals to 1 because of all the “invisible” 1’s we have in the equation such as the invisible 1 in the coefficient spot. furthermore we all know that a number times 0 equals 0 so then we are left with the invisible 1 that is the coefficient,
What I learned this week is how to convert entire radicals into mixed radicals and then mixed radicals back into entire radicals.
What you do to convert entire radicals into mixed is you start with prime factorization. as you can see I took 242 and cut it in half so now 2 x 121 is 242 and I took 121 and since it’s a perfect square I got two 11’s and since it’s a square root the answer would be 11 root 2
Turning it back into an entire radical is taking 11 and finding the squared version of it being root 121 and then you take root 2 and you multiply them giving you root 242
This here is a kind of number tree and I haven’t seen or used it before Ms. Burton showed the class and it’s basically to keep track of the order certain numbers go.
The “R” stands for real numbers and basically all numbers go under that category besides complex numbers. The “Q” with a line on top of it stands for irrational numbers and the “Q” with a line below it stands for rational numbers. The “I” below stands for integers, The “W” stands for whole numbers, and the “N” stands for natural numbers.
To explain this “number tree” better take the number 123 983 for example it fits into R,Q (with a line below it), I, W, and N.