1. All of the mixing problems that we will be dealing with will involve a “tank”.(mixing fluids in a tank)

Problem: Consider a tank which initially holds V0 gal of brine that contains a lb of salt. Another brine solution containing b lb of salt/gallon is poured into the tank at rate of gal/min, while simultaneously, the well-stirred solution leaves the tank at a rate of f gal/min

Objective: Find the amount of salt in the tank at any time t

2. The main assumption that we’ll be using here is that the concentration of the substance in the liquid is uniform throughout the tank. (in general the concentration is not the same) 3. A(t) is measuring the amount of substance , not the volume of the whole mixture, which is present in the tank at time t. Assumptions:

* rin = the rate at which the solution pours into the tank. * rout= the rate at which the mixture pours out of the tank * Cin= the concentration of salt in the solution being poured into the tank. * Cout= the concentration of salt in the solution being poured out of the tank. Remarks:

• If rin=rout then the “water level” of the tank stays the same. where V0denotes the volume of solution in the tank at time t. dAdt=Rin-Rout=rinCin-routCout
Cout=A(t)V0+rin-routt

Mixing Problems:

A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5gal/min. The well mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. What is the concentration of the solution in the tank at t=5 min?

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...1. Suppose that an open box is to be made from a square sheet of cardboard by cutting out 6-inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 486 cubic inches, find the original dimensions of the sheet of cardboard.
2. A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in 5 seconds is given by s(t) = -16t2 + 169t. At what time or times will the ball be 162 ft. from the ground? Round your answer to the nearest tenth, if necessary.
3. In Country X, the average hourly wage in dollars from 1945 to 1995 can be modeled by
f(x) = {0.074(x-1945) + 0.33 if 1945 ≤ x < 1970
{0.182(x-1970) + 0.28 if 1970 ≤ z ≤ 1995
4. A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 22 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 46 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in terms of x.
5. A rectangular garden has dimensions of 17 feet by 14 feet. A gravel path of consistent width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?
6. The volume V of a gas at constant temperature varies inversely as the...

...1. Solve
a. e^.05t = 1600
0.05t = ln(1600)
0.05t = 7.378
t = 7.378/.05
t = 147.56
b. ln(4x)=3
4x = e^3
x = e^3/4
x = 5.02
c. log2(8 – 6x) = 5
8-6x = 2^5
8-6x = 32
6x = 8-32
x = -24/6
x = -4
d. 4 + 5e-x = 0
5e^(-x) = -4
e^(-x) = -4/5
no solution, e cannot have a negative answer
2. Describe the transformations on the following graph of f (x) log( x) . State the
placement of the vertical asymptote and x-intercept after the transformation. For
example, vertical shift up 2 or reflected about the x-axis are descriptions.
a. g(x) = log( x + 5)
horizontal left shift 5
Vertical asymptote x = -5
x-intercept: (-4, 0)
b. g(x)=log(-x)
over the x-axis
vertical asymptote x=0
no x-intercept
3. Students in an English class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by S(t) = 68 - 20 log (t + 1), t ≥ 0.
a. What was the average score when they initially took the test, t = 0? Round your answer to a whole percent, if necessary.
S(0)=68-20xlog(0+1) =
68-20x0
= 68%
b. What was the average score after 4 months? after 24 months?
Round your answers to two decimal places.
-S(4) = 68-20xlog(4+1)
68-20x0.699
68-13.98
=54.02
-S(24) = 68-20xlog(24+1) = 40.04
68-20x1.398
68-27.96
=40.04
c. After what time t was the average score 50%?
Round your answers to two decimal places.
50 = 68 - 20 log (t + 1)...

...China dispelled for a while one of Australia’s major security concerns,
and détente promised a safer global strategic balance. All these developments
made Australia feel safer. On the other hand, the Vietnam War undermined
America’s role in our region and prompted, via the Guam Doctrine, a major
reduction of America’s commitments to Asian allies, including Australia. At the
same time, though for different reasons, Britain withdrew strategically from our
region too. By the end of the 1960s, the era of ‘forward defence’ was clearly
over. The good news was that our region looked much less threatening than it
had for many decades. The bad news was that our allies had made it clear that
we would have to deal ourselves with whatever problem might remain.
Well before 1970 it was clear that Australia needed a new defence policy to
deal with this new reality. Fortunately, the new challenges stimulated perhaps
the most active and informed defence debate we have ever had—in the
universities, the press and within government. Coalition Defence Ministers
including John Gorton and Malcolm Fraser started airing new ideas in the late
1960s. The debate could not help but echo the founding fathers’ debates about
imperial versus local defence priorities, but the circumstances were very different,
and so were Australia’s options. Both the nature of our regional security concerns,
and the capacity and willingness of our allies to support us had changed...

...Yr 10
Mathematics
Assignment
LCR Maths
By Adonis Chigeza
Understanding and Fluency Tasks
Task A
1. y = 1.2𝑥 + 2.57
2. Interpolation: y = -3.43
Extrapolation: y = -8.23
Task B
a) The equation for the path of the ball is h = -0.1t^2 + 0.9t + 1 (h = height, t = time)
b) The vertical height of the ball after 2. seconds2.664m
c) The maximum height reached by the ball is 3.025m
d) The time of with the ball is at maximum height of 3.025 is 4.5 seconds
e) The total time in which the ball was in the air is 10 seconds
f) The two times in which the ball was 1 metre above ground is 0 and 9
Adonis Chigeza 10C
LCR Mathematics
Problem Solving and Reasoning Task
1.
Equation: y = -1.2𝒙2 + 8.4𝒙
a. The bridge is 7 metres wides so therefore it will successfully span the river with 2
metres to spare.
b. If a yacht has a 15 metre mask it will be unable to pass safely under the bridge
because the bridge only has a vertical height 14.7 metres.
Adonis Chigeza 10C
LCR Mathematics
2. Equation: v= -0.2h2 + 2.4h
a. The horizontal distance covered by the rocket when it reached its maximum
height of 7.2 metres was 6 metres.
b. The maximum height reached by the rocket was 7.2 metres.
c. At the horizontal distance of 9 metres from the launch site, there is a 5.2 metre
wall and at that vertical distance, the rocket has a vertical distance 5.4 metre.
That is not taking to account the dimensions of the rocket, however the rocket...

...Nicolas, Fatima May D.
2014 45876
My Math Experience
When I was younger math was my favorite subject, it was something that I felt very confident
with. Unlike english, history, and literature, where I had to exert extra effort, math was the only
subject that really came naturally to me. I remember when I was a kid my dad would test me on math questions, usually about lines and figures. What kind of line intersects, what are parallel
lines? I was probably about 7 years of age, and it really impressed family friends when the
answer was correct.
In school, I always did well in math especially basic math, it was simple and it was easy.
Back then, I still have the capacity to help out other students and I was always helping out
friends with their assignments. I always got high grades on tests and I was usually done first
when it came to exams. It was really up until I started high school. Then, algebra happened, since
we didn’t have any lessons given regarding algebra (even the most basic ones) during elementary
I didn’t understand a word the teacher was saying, it was like I was reading a different language.
It was hard at first because I for one like solving problems with numbers but when it started
involving letters I knew I had to work harder because it would be different than what we have ...

...• What were the most revolutionary social and economic developments of the last quarter of the nineteenth century?
• How did different groups of Americans respond to those changes and how effective were their responses?
• What role did government play in these developments?
In the late 1900s some of the most social and economic developments were railroads, steel oil, the type writer cash register, light bulb and agriculture. The development of the railroad made it easier for immigrant to come to this country for work. This meant that there were more group of different races and cultures in America. And in some states there became an over population and city workers like police and garbage men could not keep up with the demand of so many people. Some groups mover to open land for the Homestead Act. They had hope of farming and staying on the land for at least five years as agreed but the supply and demand of agriculture did sustain so many farmer moved off the land well before their five years. The government played many different role I deescalating some issues in American history. Women and children were being worked for long hours and getting paid a little bit of nothing in return for their hard work. So the government put labor laws into place that were to protect women and children. As oil, steel and railroad industries grew so did the levels of pollution. The government again put laws that were to protect animals and the earth so that there would not...