# Week 12 – Precalc 11

For the twelfth week of Precalc 11, we started a new chapter about rational expressions and equations. In this chapter, we have so far covered how to multiply/divide and add/subtract.

To simplify this expression, we need to factor first. $\frac {(2x+2)}{(x^2+3x+2)}$

Now we can begin with factoring. $\frac{2(x+1)}{(x+2)(x+1)}$

The next step is to look at the denominator and the numerator and cancel out any of them that are identical. This has to be monomial and monomial, binomial and binomial, variable with variable, etc. $\frac {2}{(x+2)}$

Now we can simplify the expression and state the non-permissible values. The non-permissible values are the restrictions and are for the denominator. In this expression, we need to also state the NPVs of the expression before and after we converted it into an all multiplication since it had the division in it.

Therefore x≠-2 or -1.

# Week 9 – Precalc 11

For the ninth week of Precalc 11, we learned more about the Analyzing Quadratic Functions and inequalities unit.

Key Learning：

1. Vertex Form $a(x-p)^2 + q = y$
2. General Form $ax^2 + bx +c = y$
3. Factored Form $a(x-x_1)(x-x_2) = y$

We learned equivalent forms in order to solve equations by using 3 different formulas.

vertex form- $y = a (x-p)^2 + q$, where (p, q) is the vertex of the parabola, and a is the stretch value. It’s the easiest equation to graph because we are given a starting point and the pattern that it goes up by.

general form- $y = ax^2 + bx + c$,  a, b, and c are three real numbers. Once these are given, the values for x and y that make the statement true express a set of (x, y) points which form a parabola when graphed. It’s the most useless equation to graph because we are only given the y-intercept and can’t do much else unless it’s converted to one of the other forms.

factored form– $y = a(x-x1)(x-x2)$,  x1 and x2 are the opposite of the x-intercepts of a graph. This equation is useful only when given the x-intercepts and is used mostly when trying to search for a value as long as there is another point given along the parabola to substitute y and x for to find a.

# Week 8 – Precalc 11

For the eighth week of Precalc 11, we started our new unit — Analyzing Quadratic Functions and inequalities.

Key Learning：

Every quadratic function can be written in the form y = ax^2+bx+c, where a, b, and c are real numbers and a is not zero.

First, we learned the properties of quadratic functions and how to analyze the quadratic equation. We learned that when are given the quadratic equation in vertex form then we can graph the equation.

Second, we learned the quadratic equation $ax^2 + bx + c = 0$, this unit we learned $y = a(x-p)^2 + q$. This is combination of the equations $y = (x-p)^2, y = x^2$, and $y = x^2 + q$. These equations are all very important in graphing the curve the equations make.

Example：

Graph y = (x− 2)^2− 4 • Vertex = (2,4)
• x-intercept: 0 and 4
• y-intercept: 0
• opens up (happy)

# Dimensional Motion—Design Lab

#### Dimensional Motion—Design Lab

Purpose: To determine the muzzle velocity(vi) of a Nerf.

Materials:

• Stopwatch
• Nerf Gun
• Slope finder App to make sure it is 90 degrees straight up.

Procedure:

1. Fire Nerf Gun vertically, at 90 degrees, use the slope finder App to make sure it is 90 degrees straight up. Determine the time when a bullet is fired and when it lands (total time).
2. Divide time by 2 to find the time of when the bullet gets to the peak height.

Total Time/2 = Time gets to the peak height.

1. Record the data below.
2. Use the Kinematic equation to calculate the initial velocity.

Formula: Vf=Vo+at

1. Find percent difference (keep 3 sig figs) between your groups vs. other groups.

% difference= |your group data – other groups data| x 100%
Average data

Data: Nerf Gun chart

 Total time(s) Time for going upward(s) Vf(m/s) Vo=? (m/s) [upward] 1 4.20 2.11 0 20.7 2 4.13 2.07 0 20.3 3 4.36 2.18 0 21.4 4 4.05 2.03 0 19.9 5 3.80 1.90 0 18.6 Average 4.11 2.06 0 20.2

Calculations:

Show all work clearly. % difference:

% difference= |your group data – other groups data| x 100%
Average data Conclusion:

In this lab, we studied the muzzle velocity of a Nerf Gun. Because the bullet reaches the highest point and then landed at half the time the bullets reached the highest point, our time will be divided by the total time recorded. (Total Time/2 = Time gets to the peak height.) Then use the calculation formula (Vf = Vo + at) to get the initial velocity. Combining these two equations, we get the result of our initial velocity of a nerf gun is 20.2m/s

Errors in this lab came from our measurement. No measurement can be perfect. Measurements always have some uncertainty. Due to the presence of measurement uncertainty, measured values will never be equal to predicted values. This causes our error value with other groups to be around 8-18%. If we experiment on a sunny day instead of a rainy day, the results will improve, as this will not use images for the weight of the bullet. Second, the wind has a large impact on the data, which will affect the direction of the bullet, which may increase the time the bullet stays in the air. If done correctly, this will reduce our error in calculating time.

Designed by: Lina, Bianca, Grace

Oct. 15, 2019

# Ethic of Care and Environmental Ethic

1. How do you personally define an ethic of care?

I personally define the ethics of care as an attitude to taking and following by action. Care is embodied in practice and value. It’s a relationship built by emotion that can’t be separated from actual action driven by emotional impetus. It’s also about attentiveness-being aware and willing to do something, competence-having (using) the skills to able to care, and responsiveness.

1. What would be needed to create an ethic of care?

We need to be aware of what’s going on in our world and that our actions will always affect the world in some way or another, according as the butterfly effect. So, we also need to know what are the consequences of our actions, and to take a long view of these consequences, because these consequences tend to be delayed. In order to create an ethic of care, we need the above knowledge to create a relationship, and taking action on it.

1. What would we have to believe about the environment to care for it? How should we see it?

The environment around us is an essential part of human survival and development. I would like to believe that people who do not care about the environment, simply do not understand how important it is to all of us and that it does not affect them directly, these are my reasons why we should be concerned and care about the environment. We should see it as an ongoing and serious global problem that concerns every one of us, and think long term about our future generations.

1. How would we act if we cared about the environment? – give scenario

We can show our care for the environment in our daily life through some actions within our power.

-Reduce the use of disposable products, such as we can use our own reusable bags instead of supermarket’s disposable plastic bags.

-Limit the amount of bottled water we drink, preferably with a reusable water bottle. Statistics show that more than one million bottles of drinking water are sold every minute worldwide. Bottled water is one of the main sources of plastic waste.

Resource shortage is one of the most serious environmental problems in the world. For example, the paper is made from wood pulp, so we can protect the forest by saving paper. Save water, electricity, food and so on is saving the resource for our sustainable development.

1. What would be different about the world if everyone adopted this ethic of care towards the environment? Benefits and drawbacks?

If everyone adopted this care for the environment, maybe there wouldn’t be so many environmental problems in the world. Global warming and climate change may be solved or not happening at all, and there won’t be so many places suffering from air pollution that we and our future generations will live in a better world, a healthier planet.

The disadvantage is that it may affect the interests of some companies or even the development of some countries. For example, If we stop drinking bottled water, using disposable plastic bags and disposable tableware in order to reduce the pollution of plastic waste; If we force the closure of some heavy industrial plants to reduce air pollution, what will happen to the factories that produce these things and the people who work there and it will certainly affect the interests of the companies that own them. There are also some of the country’s main economic source is exported oil fuel or other non-renewable resources, if we in order to protect the mineral resources, reduce environmental pollution, protect the ecological balance of earth and the basic structure, then the export trade and economic development in these countries will be affected from will affect the development of the whole country.

1. Should we adopt an ethic of care towards the environment?

To some extent, we should adopt an ethic of care towards the environment, which will make us more aware of these environmental problems and recognize what the consequences are, thus we will take some actions and make changes in our daily life. But not all people judge themselves by the same ethics, everyone has different values, we can’t hold everyone to one standard. However, In my personal opinion, I’m in favor adopt an ethic of care towards the environment.

# Week 4 – Precalc 11

For the fourth week of Precalc 11, we continued studying about “Radical Operation and Equations” unit.

First, we learned how to Multiply & Divide Radicals.

When we are multiplying radicals (with the same index), we need to multiply under the radical first, and then multiply in front of the radical (any values multiplied times the radicals).  When we are dividing radicals (with the same index),  we need to divide under the radical first, and then divide in front of the radical (divide any values multiplied times the radicals).

And also to divide radical expressions with the same index, we use the quotient rule for radicals. If a and b represent nonnegative numbers, where ,  then we have:  # Week 3 – Precalc 11

For the third week of Precalc 11, we started our new unit “Radical Operation and Equations”.

We learned how to write an entire radical to a mixed radical and how to write a mixed radical to an entire radical. And we also learned how to add or subtract radicals. Like terms are radicals with the same index and radicand, these are the only radicals that can be + or- . When there is a variable in the radicand, you must specify what type of number (positive or negative) is needed to make the radical defined, for √ , the radicand must be a positive number.

# Week 2 – Precalc 11

For the second week of Precalc 11, we continued studying about “Roots and Powers”.

We learned power with positive rational exponent and negative rational exponent. We also learned Exponent Laws and Order of Operations which is applying the order of operations and exponent laws to evaluate numerical expressions and simplify algebraic expressions. We can recall “BADMAS” for remembering the order：

B (brackets)  E (exponents)  D/M (divided or multiply )  A/S (add or subtract)

And through the skill check 2, I noticed an exponent law that is very easy to make mistakes, that is !!! $a^0$ = 1 !!!