Polynomials

We started factoring polynomials.

Which in this case is just doing monomials,binomials, trinomials backwards.

So for example in the picture. We found the common greatest factor of each of the 3 numbers which is 24 and GCF of the variables.

We put that to the side, and we put the rest in the brackets. Afterwards we setup the negatives and positives to equal the beginning expression.

Polynomials

We started polynomials, introduction to degrees, multiplication between monomials and binomials.

Like in Degrees, we learned that their the highest amount of variables in the expression, from the expression there can be multiple terms. In each term may contain a variable, if not it becomes a constant term. The highest amount of variables in the term has the ‘degree’.

like in the image above^^^^^^

in monomials and binomials we use distributive property as well as zero pairing.

As in like x(a-b)  or (a+b)(c-d)

x(a)-x(b)  a(c-d)+b(c-d)

TRIGONOMETRY 4.1

The New Chapter we started is consisted of what makes up a triangle to its angles and in relation with its sides.

Day 1 we learned to obey the SOH CAH TOA ritual to help us with remember what to use.

As S=Sine C=Cosine T=Tan

O= Opposite The opposite of the angle which it is faced

H=Hypotenuse The Slanting side which is the largest of the 3 sides, and always against the 90* angle.

A= AdjacentThe Side next to the opposite and always  countered against the Hypotenuse.

As for example in Sine, we use Opposite/Hypotenuse to get the desired angle.

There’s also the Trigonometry ratios, which consists of the SOH CAH TOA rule aswell,

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for ex: we want to find the height, which in this case is the opposite, because it’s across from the working angle=40*

So we would use Tangent, since we want to use the Opposite/Adjacent.

Tan40*=Opposite/75ft

Opposite=tan40*75ft

Opposite=62.9ft

Working Backwards

We can also work backwards from this stance, if we have tanX=62.9/75

tanX=62.9/75

tanX=0.84

X=0.84*(Tan-) Tan negative is what we click on the calculator to find the angle.

X=40*

We can also find the Hypotenuse, whether it’s using Pythagoras or simply continuing to use Trigonometry

Simply Shifting to towards using Cosine which implements the Adjacent/Hypotenuse can give find us any of the two. The most important key is to fill use where the application is best fitted.

So we would use Cos40*=75/H

Cos40*=75/H

H=75/(Cos40*)           Always figure out the cos of 40 first

H=75/0.77

H=97.4ft

Conclusion: Using SOH CAH TOA in the correct application will give you the right answer. But it must be the right application.

Sine= Opposite/Hypotenuse Cosine=Adjacent/ Hypotenuse  Tangent=Opposite/Adjacent

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The Last Unit of Measurement

as the surface area is 4piRsquared

In the last chapter of measurements before our test, we learned how measurements could be implemented into objects, such as finding the volume or surface area, then swapping the units( like imperial to metric) in order to finish the question. Aswell as questions like ” if …. is 11 inches long …. they need to make a goal thats 8 inches long…” page 195 #3 We would need to know how many inches are in 1 yard. 36/11 then times 8 to get 26.

From Fractional exponents to radicals and vice versa.

Today we learned that as exponents can be considered negative, it can also be considered into a fraction. Where the denominator is always the index and the numerator is always the power to the radicand or radical.

In a. you can see that the radical has an index of 2, since in the fraction form the denominator is also two. In class the easiest way to remember this formula is ‘flower power’

This system works for everything, as long as it’s in the brackets, everything inside will be rooted. Unless then only the base of the exponent will be rooted.

How Each Question was delivered:

a: 3 to the power of 1/2 follows ‘flower power’ as the denominator follows as the INDEX and the numerator follows as the EXPONENT, creating a radical

b: 7 to the power of 3/4 follows the same thing, but it only shows that the exponent can be on the 7 or outside the bracket

c: x to the power of the -3/2, the first step for me would to change it into something positive, so you would flip it upside down then following step A or B to complete the question

d: a squared and b squared can be resolved by transforming the terms inside the brackets under the same radical by using the same methods in a or b .  Another popular way is to multiply it by everything inside.  a squared multiplies 1/2 and repeats for b. which would equal them out since 2 x 1/2=1 so the answer in the end is the same no matter which route you take.

This week was about roots, squared,cubed–any and how to solve them as well as all their components.

In the question above is shown how to change a mixed radical  into an entire radical.

The part not show is the reason why 3×3 is because 3 multiplies itself twice because in order to function as a root it must be squared.

We also learned all the functions, names, and parts of a Radical.

Prime Factoring.

Ms. Burton’s C Block

Prime Factoring is factoring a number into smaller numbers that are only divisible by itself and 1.

In the image begins with 1050, but slowly dividing it by prime numbers can slowly reach its last dividable number which should also be a prime number. Allowing you to count all the prime numbers available; which is the 2,3,5,5,7. This is one of many ways to factorize numbers.