Search & Filtering
4+4=
A learner subtract by using the vertical algorithm.
What calculation error did the learner make in subtraction
12. A large reaction vessel is filled with water. In the morning X m' are added to the vessel. More water is added to fill the vessel in the afternoon. Water is added for Y hours at a rate of Z m°/minute a. Write an algebraic expression for T, the total amount of liquid the reaction vessel can take. Show your working/ reasons (in words or using mathematics).
b. If 20,000 m° is pumped in during the morning. Lt takes 6 hours to complete filling the vessel in the afternoon at a rate of 1000 m°/minute, what is the capacity of the reaction vessel in m°?
a) Find all the units of Z[ − 7]. b) Check whether or not < 8x + 6x − 9x + 24 > [x] 3 2 Q is a field. c) Construct a field with 125 element
a) Using Cayley’s theorem, find the permutation group to which a cyclic group of
order 12 is isomorphic. (4)
b) Let τ be a fixed odd permutation in .
S10 Show that every odd permutation in S is
10
a product of τ and some permutation in .
A10 (2)
c) List two distinct cosets of < r > in ,
D10 where r is a reflection in .
D10 (2)
d) Give the smallest n ∈ N for which An is non-abelian. Justify your answer.
hich of the following statements are true? Give reasons for your answers. i) If a group G is isomorphic to one of its proper subgroups, then G = Z. ii) If x and y are elements of a non-abelian group (G, ∗) such that x ∗ y = y ∗ x, then x = e or y = e, where e is the identity of G with respect to . ∗ iii) There exists a unique non-abelian group of prime order. iv) If (a, b)∈A× A, where A is a group, then o((a, b)) = o(a)o(b). v) If H and K are normal subgroups of a group G, then hk = kh ∀ h ∈H, k ∈K.
Convert 0.8 to the common fraction in its simple form. Show all necessary working.
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
For this written assignment, answer the following questions showing all of your work.
1. Find the domain of the function using interval notation.
2. Sketch a graph of a piecewise function. Write the domain in interval notation.
[Suggestion: for example, go to www.desmos.com/calculator and write
for {-1 ≤ x ≤ 1}
and
y = 3x - 2 {1 ≤ x ≤ 3}
Then choose your own functions and have fun.]
3.
The cost in dollars of making x items is given by the function C(x) = 10x + 500.
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
b. What is the cost of making 25 items?
c. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?
Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”.
For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”.
Does this equation determine a relation between x and y? Can the variable x can be seen as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y= h(x)? If these are possible, then what will be the domains for these two functions? What are the graphs of these two functions?
Are there points of the coordinate axes that relate to (0, 2) by means of R?
