rpahlevanlumath10A

Multiplying Polynomials

November 6, 2016 — Leave a comment

This week in class we learned how to multiply polynomials by using a method called FOIL.
FOIL is a type of distributive property.

FOIL stands for First term in each brackets, Outside terms, Inside terms and Last terms in each brackets. (First, Outer, Inner, Last.)

First- multiply the terms which comes first in each binomials.
Outer- Multiply the outer most terms in the products.
Inner- multiply the inner most two terms.
Last- multiply the terms which comes last in each binomials.

Then simply by collecting like terms if there are any.

For example:

(a^2 + b) (a + b)
= (a^2)(a) + (a^2)(b) + (b)(a) + (b)(b)
=       first                               outer                  inner        last
=  a^3 + a^2b + ab+ b^2

 

Finding a Missing Side of a Right Triangle

November 4, 2016 — Leave a comment

To find a missing side of a right triangle, you’ll need 1 side and 1 angle.
To find a missing angle of a right triangle, you’ll need 2 sides.

There are 2 ways to solve for a missing side of a right triangle. By using either SOH CAH TOA or if there are already 2 sides, you can use pythagorean theorem.

First, label the sides in respect of the angle you’re using. Once you’ve labeled decide which trig function to use.

SOH       CAH       TOA
(Sin: \frac{O}{H}) (Cos: \frac{A}{H}) (Tan: \frac{O}{A})

img_1844

To solve this equation I will be using Cos for we’re looking for adjacent and we have the hypotenuse. Cosine: \frac{A}{H}

\cos45^\circ=\frac{x}{36}
(36) \cos45^\circ=\frac{x}{36} (36)
(36) \cos45^\circ = x
x = (36) \cos45^\circ
x = 24.7487 cm
x = 25cm (rounding to the nearest cm)

 

Converting between SI and Imperial Units

November 4, 2016 — Leave a comment

We learned how to convert measurements between Imperial and SI units.

Converting between,
SI (metric) to SI, Imperial to Imperial, SI to Imperial and vice versa.
SI is the measurement system that is used in Canada and most country.
Imperial measurement system is used in United States, Liberia and Myanmar (Burma).

SI measurement system uses (mm, cm, m, etc)
Imperial measurement system uses (in, ft, yd, etc)

Some examples

Converting within imperial

12 ft 3 in to inches
12ft x \frac{12in}{1ft}
12 x \frac{12in}{1} = 144 in
144 + 3 = 147 in
12 ft 3 in = 147in
There are 12 inches in 1 foot. You put whatever unit you want to get rid of in the denominator.

Converting within SI

35mm to metres
35mm x \frac{1m}{1ooomm}
35 x \frac{1m}{1ooo} = \frac{35m}{1ooo}
\frac{35m}{1ooo} = 0.035 m
35 mm = 0.035m

Converting SI and Imperial

8ft 3in to metres
feet to inches to centimetres to metres
8ft x \frac{12in}{1ft} = 96in
96in + 3in = 99in
99 x \frac{2.54cm}{1} = 251.46cm
251.46cm x \frac{1m}{1oocm} = \frac{251.46}{1oo}
\frac{251.46}{1oo} = 2.5146m
8ft 3in = 2.5146m

Finding GCF and LCM

September 16, 2016 — Leave a comment

The method we used to find the greatest common factor and the lowest common multiple in class is by using prime factorization and finding all the prime factors.

Another method I found for finding the greatest common factor was by listing all the factors of both numbers then choosing the greatest one they have in common.
for example finding the great common factors between 135 and 185.
135= 1, 3, 5, 9, 15, 27, 45, 135…
185= 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270…
In this case the greatest common factor between the two would be 135.

Another method I found for finding the lowest common multiple was by listing all the multiples and finding the first one they have in common, making it the lowest common multiple.
For example finding the lowest common multiple between 125 and 225.
125= 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250, 1375…
225= 225, 450, 675, 900, 1125, 1350, 1575…
In this case the lowest common multiple between the two would be 1125.

Personally I prefer the prime factorization method because it’s easier to do, much faster and less complicated.