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Newtons Laws

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Newtons Law #1

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is represented in how the bottle on the roof moves with the car until the car stops, this in turn, changes the bottle’s state but continues to move it forward.

Newtons Law #1 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

Newtons Law #2

The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass over velocity) per change in time. This is represented in how we push the car to move it forward, subjecting an external force to change the velocity.

Newtons Law #2 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

Newtons Law #3

The third law states that for every action (force) in nature there is an equal and opposite reaction. More explained if object A exerts a force on object B, object B will exert the same force back to object A. This is represented in the video by how the wheels of the car when accelerated push against the ground, force is put into the earth and at the same time is pushed back into the car; however, because of the difference in size between earth and the car, earth becomes unaffected by the force while the car is sent forward leading to acceleration.

Newtons Law #3 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

Week 5- Factoring polynomials

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This week, we spent reviewing factoring polynomials.

ex: x²+12x+20

Notice that this equation is rational. This means that we can easily factor this equation. To factor this equation, we want to look at which 2 numbers multiply into 20 AND add into 12. If we look at the numbers 10 and 2, we see that if you multiply them, they equal 20 and when you add them, they equal 12. This means that these 2 numbers will be used to factor. (x+10) (x+2) is the answer once factored. Once expanded, the product will be x²+12x+20. This means is a good way to make sure the factoring was done properly.

Week 3-Radicals

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This week, we started working with radicals. This week, I wanted to show how one would simplify radicals. I feel like this will help myself when studying for the final.

Ex. \sqrt{27}

when simplifying radicals, you want to look at the number you are using, in this case, 27, and finding what perfect square goes into it. For 27, it is 9 because 9×3=27.

We can square the 9 and but it outside the root and keep the other 3 on the inside because it cannot be squared. The simplified version of \sqrt{27}  is 3\sqrt{3}

Week 2- Geometric Series

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This week, we started by learning how to find a common ratio for geometric series’. Geometric series are when one number is multiplied by the same number each time.

Ex. 3, 9, 27

To find the common ratio (r.) We have to divide the first term by the second term. \frac{9}{3} = 3

`This means that the common ratio is now 3. When we multiply each term by 3, the geometric series continues correctly.

 

Week 1- Arithmetic Sequences

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This week, we worked with arithmetic sequences.

2,4,6,8,10…

Each of the numbers above are considered terms. The number 2 is considered t_1

Part 1:

When finding a term, we use the formula: t_n = t_1 + (n-1)d  (d represents difference between terms.)

For finding term 50, we will use this formula.

t_{50} = 2 + (50-1)2

t_{50} = 2 + 98

t_{50} = 100

 

Part 2:

When finding the sum of all terms, we use the formula: s_{50} = \frac {n}{2} + ( t_1 + t_n )

I will be using the same sequence from above to find the sum.

s_{50} = \frac {50}{2} + ( 2 + 50)

s_{50} = 25+ 52

s_{50} = 77

 

 

 

Math 10 week 10- Updated

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This week we learned how to factor polynomials. Factoring polynomials is almost like reversing the question.

Ex. 7x^2 -49

In this example, we want to remove the greatest common factor. We know that 7 goes into 49 7 times.

We can then move the 7 outside the brackets and divide 49 by 7. This looks like this: 7( x^2 -7)

Now, to make sure it is correct, we can expand the polynomial by multiplying all the values in the brackets by 7. This will give us 7x^2 -49 (the original question!)