## Assume that (S_n) and (t_n) are sequences of real numbers such that (S_n) is bounded and limn→∞ t_n = −∞.

Question Assume that (S_n) and (t_n) are sequences of real numbers such that (S_n) is bounded and limn→∞ t_n = −∞. Prove that limn→∞ t_n S_n^2 = −∞.2. Let S ⊂ R a bounded non-empty subset of the real numbers such that inf S /∈ (not included) S. Prove that there exists a sequence (Xn) ⊂ S such that limn→∞ Xn = inf S.

## Which of the following functions are equivalent? Explain how you know.

Question Which of the following functions are equivalent? Explain how you know. Question 1 f(x)=3(4x-2) 8 and g(x)=2(6x 1)Question 2f(x)=x^2-8x 15 and g(x)=(x 3)(x 5)Question 3f(x)=5(x^2 3x-2)-(2x 4)^2 and g(x)=x^2-x-26Question 4f(x)=x^3-y^3 and g(x)=(x-y)(x^2 y^2)Question 5f(x)=6x(5x-3)(x 2) and g(x)=10(3x^3 4x^2) 2x(x-18)Simplify each of the following.Question 6(-x^2 2x 7) (2x^2-7x-7)Question 72(3a-5)(4a-7)Question 8(2x^2y-3xy^2)(4xy^2 5x^2y)Fully factor each of the following.Question 96m^2 2m^3Question 10-14m^2n^10 14m^7n^3-63m^3n^5Question 11x^2 15x-16Question 123x^2 24x 45Question 136x^2-13x 6Question 1412x^3-60x^2 75xQuestion 152x^4-162Question 16Is there a value of a such that f(x)=9x^2 4 and g(x)=(3x-a)^2 are equivalent?Explain.

## A patient is given a dosage Q of a drug at regular intervals of time T . The concentration

Question A patient is given a dosage Q of a drug at regular intervals of time T . The concentration of the drug in the blood has been shown experimentally to obey the lawdCdt = −keC(a) If the first dose is administered at t = 0 hr, show that after T hr have elapsed, theresidualR1 = − ln(kT eQ)remains in the blood

## Express each of the following expressions in simplified form. 1

Question Express each of the following expressions in simplified form. Question 1 √75Question 25√200Question 3-√90 5√40Question 412√27-13√200-3√48 7√8Question 5-√5(2√10)Question 65√14(4√2)Question 7-2√5(1 2√5)Question 8(2-3√11)^2Question 9The measure of the area of a square is 132 square centimetres. Express the length of the side of a square, in simplified radical form.Question 10If two sides of a right-angled triangle are 4 and 6, respectively, determine the hypotenuse in simplified radical form. Hint: a^2 b^2=c^2Question 11Find a simplified expression for the area of the shape below. Hint: A= bh .

## Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 7

Question Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 7 7% per year (data from 2010 to 2011). If emissions continue to increase at this rate, about how much higher will total emissions be in 2025 than in 2010?Using the approximate formula, emissions will increase by a factor of between 2010 and 2025Using the exact formula, emissions will increase by a factor of between 2010 and 2025(Round to two decimal places as needed.)

## . The eight symmetries of a square

1 2 4 3 form a group denoted

Question . The eight symmetries of a square

1 2 4 3 form a group denoted D4. Let r be a 90◦ clockwise rotation and f a horizontal ﬂip (that is, about a vertical axis). It is not diﬃcult to show that D4 = hr,fi. (a)find all 8 actions of D4 using r and f and draw a Cayley diagram using these two actions as generators. (b) Let g be the reﬂection of the square that ﬁxes the lower-left and upper-right corner. Which of the eight actions in D4 is g equal to? Which action is fg? (c) Draw a Cayley diagram of D4 using f and g as generators. (d) Find all minimal generating sets of D4. [Hint: There are 12.] (e) Find a minimal generating set of D6 (the 12 symmetries of a regular hexagon) that has three actions

## Ishah spins a fair 5-sided spinner. She then throws a fair coin.

Question Get Answer Ishah spins a fair 5-sided spinner. She then throws a fair coin. (i) List all the possible outcomes she could get. The first one has been done for you(1, H),(5)Ishah spins the spinner and tosses the coin. (1)Work out the probability that she will get a 2 and a head._______________________________________________________________________________________________________ A bag contains Red, Green and Yellow balls. A ball is taken at random from the bag.The probability that it is Red is 0.35 and the probability that it is Green is 0.4Find the probability that ball selected is:(i) Yellow (1)(ii) Not Red (1)