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Activity 4 4.1 Consider the linear sequence: \( 5 ; 8 ; 11 ; b: 17: \ldots \) 4.1.1 Write down the value of \( b \). 4.1.2 Determine the \( n^{t h} \) term of the sequence. 4.1.3 Calculate the value of the \( 15^{\oplus} \) term of the sequence. 4.1.4 Which term of the sequence is equal to 83 ? Activity 5 5.1 The first term of a linear number pattern is 92 and the constant difference is -4 . 5.1.1 Write down the values of the second and third terms of the pattern. 5.12 Determine an expression for the \( n^{\text {th }} \) term of the number patterm. 5.13 Determine the value of the eighteenth term. S.1.4 If \( T_{p}+T_{q}=0 \), determine the value of \( (p+q) \). TUTORLAL 2 Activity 1 1.1 Given the finite linear number pattern: \( 12 ; 17 ; 22 ; 22 ; \ldots ; 172 \). 1.1.1 Deternine the formula \( n^{\text {th }} \) term of the pattern. 1.1.2 Calculate the value of \( T_{12} \). 1.1.3 Deternine the number of terms in the pattern. 12 Given the first four terms of a linear pattern: \( 3: x: y: 30 \)

5. MP Use Tools Write an expression with a single exponent that is equivalent to \( 8^{-4} \cdot\left(8^{2}\right)^{4} \). State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

Divide. \[ \left(14 x+20 x^{3}+11+15 x^{2}\right) \div\left(5 x^{2}+2\right) \] Write your answer in the following form: Quotient \( +\frac{\text { Remainder }}{5 x^{2}+2} \). \( \frac{14 x+20 x^{3}+11+15 x^{2}}{5 x^{2}+2}=\square+\frac{\square}{5 x^{2}+2}+\square \times \square \)

\( \lim _ { x \rightarrow 4 } \frac { x + 1 } { x - 2 \sqrt { a x + b } } = + \infty \quad b = ? \)

22. Дадени са числата \( x \) и \( y \), като: (1) \( x \) е неизвестно число в равенството \( 3^{-2}: x-2 \frac{4}{5}=\left(-\frac{3}{10}\right)^{7} \cdot\left(3 \frac{1}{3}\right)^{7}-0,8 \); 2) \( y \) е такова, че стойността на израза \( 3 \cdot y-\left|\frac{-8-\left(-2^{2}\right)}{8}\right| \) е с 4 по-голяма от стойността на израза \( \frac{1}{2} \) . Намерете \( x \). . Намерете \( y \). С Солко \( x \) е по-малко от \( y \) ? С С колко процента \( y \) е по-голямо от \( x \) ? Намерете стойността на израза \( x^{y-3} \cdot\left(\frac{x-y}{3}\right) \).

\( 3 y+x=2 \) and \( y^{2}+x=x y+y \)

9. \( \left(\frac{1}{4}\right)^{2} \)

2. What is the SI unit of energy?

1. What is the formula for calculating the speed of an object?

answers: 1.. \( x+y=10 \) \[ x-y=2 \] 2. \( x+y=5 \) 3. \( 2 x+3 y=11 \) \( 4 y-2 x=10 \) 4. \[ 3 x+2 y=13 \] \[ 2 x+3 y=18 \] \[ 8 x=7-3 y \] 6. 5. \( 8 x=7-3 y \) \( 3 x+4 y=3 \) \[ 9 y=-20 x+13 \] \( 6 x=7-10 y \) 7. \( 2 y=3 x+3 \) 8. \( 3 y-4 x=4 \) \( 2 y=x \) \( 8 x-1=-2 y \) 9. \( 4 y=-x \) 10. \[ \begin{array}{l} 3 y+6=6 x \\ x=2 y-2 \end{array} \]

\( \int ^ { \infty } \frac { 1 } { x + 1 } \)

\( \left. \begin{array} { l } { f ( x ) = x ^ { n } } \\ { f ^ { \prime } ( x ) = n x ^ { n - 1 } } \\ { \int x d x = x ^ { 2 } \quad \int 2 x d x } \\ { = \frac { x ^ { n + 1 } } { n + 1 } } \end{array} \right. \)

3. Why are fireworks so dangerous? a. They produce carbon monoxide that suffocates people b. They produce poisonous gases. c. They can blow up and hurt people. d. They may spread diseases. 4. Why would road flares be red? a. Red flares are the prettiest ones. b. Red flares show up well at night. c. Red flares are the only color that can be made. d. Red flares make more noise than other colors.

Divide. \[ \left(12 x^{3}-24 x^{2}+6 x+10\right) \div\left(3 x^{2}-3 x\right) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)

\[ \left(3 x^{2}+26 x+36\right) \div(x+7) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)

26 Fireworks Do you enjoy watching fireworks? Do you like their colorful sparks and loud noises? Fireworks start out as hollow cardboard tubes filled with gunpowder. A fuse sticks into this gunpowder. The fuse is a thick cotton string. It's been soaked in saltpeter. When a flame lights the fuse, it burns the gunpowder. This makes the rocket shoot into the air. Then the gunpowder lights a smaller packet of gunpowder. This blows up the cardboard tube. It ignites tiny firecrackers at the top of the rocket, too. What makes the different colors? Small amounts of chemicals are added to the gunpowder. Sodium makes yellow sparks. Copper makes blue sparks. Charcoal gives the fireworks sparkling tails. Fireworks are not just pretty. They are dangerous. If they blow up near you, you i can be badly hurt. That's why some states won't let stores sell fireworks. That way, ni only experts can set them off. Fireworks have other uses, too. You may : have seen red flares on a road around an. accident. They are a different kind of firework. They burn for a long time and do not blow up. Check Your Understanding 1. Which chemical makes yellow fireworks? a. sodium c. copper b. charcoal d. calcium

2. Derive the equation for the period T and frequency f for a simple pendulum ( 6 marks)

48 Determina l'equazione della retta \( t \) tangente in \( T(1 ; 3) \) alla circonferenza con centro in \( C(-2 ; 0) \), quii scrivi l'equazione della parabola con asse di simmetria parallelo all'asse \( y \), tangente in \( T \) alla retta \( t \) e passa per il punto \( A(-1 ; 9) \). Trova l'equazione di una retta parallela all'asse \( y \) che interseca la parabola in \( P \), retta \( t \) in \( Q \) in modo che l'area del triangolo \( P Q T \) sia uguale a 108 , \[ y=-x+4 ; y=x^{2}-3 x+5 ; x=-5 \vee x= \]

Write a formal letter in response to one of the following topics. 12.1 You have bought an article of clothing from a fashion store. There is something wrong with the garment and you would like your money back. Write a letter to: The Manager, Fabulous Fashions, P.O. Box 188 , Durban, 4000 , giving details about the defective garment and requesting a refund.

\( \lim _ { x \rightarrow . ^ { - } } \frac { \sqrt { 1 - \sqrt { 1 + x } } } { x } \)

(8) \( 3^{-x}=\frac{1}{243} \)

If both of the waves pictured above are sound waves, the pitches they make would be different. The pitch of a sound wave describes how high or low a sound is. A sound that is very high is described as high pitched, while a sound that is very low is described as low pitched. The pitch of a sound is related to the wavelength and frequency of a sound wave. If a sound wave has a greater frequency (a smaller wavelength) it will make a higher pitched sound, just like the wave on the right. If a wave has a smaller frequency (and a bigger wavelength) it will make a lower pitched sound, like the wave on the left.

Divide. \[ \left(32 y z^{2}-8 y^{7} z^{7}\right) \div\left(4 y^{5} z^{3}\right) \]

If \( \sin \theta=\frac{12}{13}, 0<\theta<\frac{\pi}{2} \), find the exact value of each of the following. \( \begin{array}{lllll}\text { (a) } \sin (2 \theta) & \text { (b) } \cos (2 \theta) & \text { (c) } \sin \frac{\theta}{2} & \text { (d) } \cos \frac{\theta}{2} & \text { (e) } \tan 2 \theta\end{array} \) (f) \( \tan \frac{\theta}{2} \)

6. \( 8^{3} \)

Use any model to show the division expression. Then write the quotient. \( \begin{array}{ll}\text { (1) } 35 \div 5 & \text { ( ) } 21 \div 7\end{array} \)

QUESTION 2: Summary Read Text B and summarise the seven key points of the passage. Your summary must be in the form of one paragraph, using no more than 90 words. Provide an accurate word count at the end of the summary. Your language must be precise and in an appropriate register. Use your own words. TEXT B Who is responsible for the greatest change to our language? Turns out it's teenage girls. "If you're on a bus, what you should do is position yourself as close as possible to a group of young women and then shut your eyes and listen. What you hear is the future of language in your community," says Sali Tagliamonte, professor of linguistics at the University of Toronto. And while young people often lead the charge with language, Dr Tagliamonte points out that young women tend to be at least a generation ahead of young men, "Young women tend to be the drivers of linguistic change and progress." The discovery that young women drive linguistic change is not new. More than two decades ago, William Labov, the founder of modern sociolinguistics studies, observed that women lead 90 per cent of linguistic change. In 2003, linguists surveyed 6,000 letters. The study found there was a quicker uptake of new language contained within the letters written by women compared to those written by men. "What we see are the same types of patterns in language use, as we tap into contemporary language change," Dr Tagliamonte says. While some might celebrate linguistic change, others can find it threatening. "When language changes, it's a complex adaptive system. It is not the same change from one generation to the next, as each generation distinguishes itself from another," Dr Tagliamonte says. As she explains it, the teenage population is reluctant to sound like their parents and vice versa. One mother's main frustration is the Americanisation of phrases that her teenage daughters adopt. or example, they refer to "birth control" rather than "contraception" and "gas" instead of "petrol". r Tagliamonte says when we impose social value judgements on language, it's not because nguage is inherently good or bad. "It's because we make judgements about other people based i the way they talk." t, it seems language will inevitably continue to evolve.

\( y=\sinh (x) \)

3) \( \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} \)

2) \( \lim _{x \rightarrow 0}\left(\frac{x e^{-x}}{3 e^{x}-3}\right) \)

1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \)

3) \( \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} \)

2) \( \lim _{x \rightarrow 0}\left(\frac{x e^{-x}}{3 e^{x}-3}\right) \)

1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \)

\( \ddot { x } + \omega ^ { 2 } x = 0 \)

1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \) 2) \( \lim _{x \rightarrow 0}\left(\frac{x e^{-x}}{3 e^{x}-3}\right) \) 3) \( \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} \)

1. Let's begin with a review of several terms that you may already know. Define: gene: locus: gamete: male gamete: female gamete: asexual reproduction: sexual reproduction:

4 How does ithe title help you infer the theme of this welection? Use ideas from the selection. 5 Why was Lily remembering that Thompson and sons had recently shut down important in developing a theme of this story?

Tom walks 1.5 km every day. How far does he walk in 7 days? Write your answer in meters.

7 8) Written as a product of its prime factors, \( 588=2^{2} \times 3 \times 7^{2} \). (a) Find the smallest positive integer value of \( k \) such that \( 588 k \) is a perfect cube. Answer \( k= \) \( \qquad \) (b) Express 90 as a product of its prime factors.

The last kind of circuit is a combination circuit. A combination circuit has light bulbs arranged in both series and parallel. In one combination circuit, for example, current might travel through one branch where two components are arranged in series, and then travel through another branch with multiple components arranged in parallel.

Rita deposits \( \$ 600 \) into an account that pays simple interest at a rate of \( 5 \% \) per year. How much interest will she be paid in the first 6 years?

3. Given that \[ f(x)=\left\{\begin{array}{cc}1 \sqrt{x}, & 0<x<1 \\ 0, & \text { elsenhere }\end{array}\right. \] a) Evaluate k . b) Evaluate \( \mathrm{P}(0.3<\mathrm{X}<0.6) \) using the density function.

Use the distributive property to find the product. \[ \begin{aligned} 2 \cdot 30.8 & =2 \cdot(30+\square)+(2 \cdot \square \\ & =(2 \cdot \square) \\ & =\square \\ & =\square\end{aligned} \]

Use the distributive property to find the product. \[ \begin{aligned} 2 \cdot 30.8 & =2 \cdot(30+0.8) \\ & =(2 \cdot 30)+(2 \cdot 0.8) \\ & =\square \\ & =\square\end{aligned} \]

Evaluate. \[ \frac{2}{3}+\frac{5}{6} \cdot \frac{1}{2} \] Write your answer in simplest form.

A graphing calculator is recommended. When a foreign object that is lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward, causing an increase in pressure in the lungs. At the same time, the trachea contracts, causing the expelled air to move faster and increasing the pressure on the foreign object. According to a mathematical model of coughing, the velocity \( v \) (in \( \mathrm{cm} / \mathrm{s} \) ) of the airstream through an average-sized person's trachea is related to the radius \( r \) of the trachea (in cm) by the function \[ v(r)=3.1(1-r) r^{2} \quad \frac{1}{2} \leq r \leq 1 . \] Determine the value of \( r \) for which \( v \) is a maximum. (Round your answers to two decimal places.) \( r=\square \mathrm{cm} \)

The hammer throw is a track-and fuid event in which 3730 -gg ball (the hammer) is whirled around in a circle several times and released. It then moves upward on the familiar curved path of projectile motion and eventvally returns to the zround some distanca away, The world record for the horizontal distance is 86.75 m , achieyed in 1986 by Xuriy Sodym. Ignore air resigtance and the fact that the ball was released above the ground rather than at ground leyel, furthermore, assume that the ball is whinhed around a circle that has radius of 277 m and that its velocity at the instant of release is directed 56.59 above the horizontal. Find the magritude of the centripetal force acting of the ball just prior to the moment of release, Number \( \square \) Units \( \square \)

\( f(x)=\frac{1}{4} x-8 \) If \( f(X)=-\frac{7}{2} \), find \( X \)

A camera has a listed price of \( \$ 845.98 \) before tax. If the sales tax rate is \( 7.5 \% \), find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.

25 Uma fábrica de motocicletas realizou uma pesquisa de mercado com 400 jovens maiores de idade, concluindo que, precisamente: - 283 dos entrevistados já haviam dirigido automóvel; - 127 dos entrevistados já haviam dirigido motocicletas; - 67 dos entrevistados não haviam dirigido nenhum dos dois tipos de veículo. Quantos dos jovens entrevistados já haviam dirigido os dois tipos de veículo?

Multiply. \[ \frac{5}{9} \times 72 \] \( \square \)

What are the vertex, focus, and directrix of the parabola whose equation is \( y-4=\frac{1}{4}(x-7)^{2} \) ? vertex \( =(\square) \) focus \( =(\square \)

1. ึ่าหนดให \( \cos A=0.8 \) จงหาค่าของ \( \cot ^{2} A \cdot \tan A(2 \) คะ

Yolanda bought a sofa on sale for \( \$ 341 \). This price was \( 38 \% \) less than the original price. What was the original price?

On November 1. Jovel Company loaned another company \( \$ 300,000 \) at a \( 7.0 \% \) interest rate. The note receivable plus interest will not be collected until March 1 of the following year. The company's annual accounting period ends on December 31 . The amount of interest revenue that should be reported in the first year is:

คำสั่ง ให้นักเรียนแสดงวิธีทำทุกข้อ 1. กำหนดให้ \( \cos A=0.8 \) จงหาค่าของ \( \cot ^{2} A \cdot \tan A \) (2 คะแนน \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \)

Complete the equation for the circle with center \( (-2,-4) \) and radius 9 . \( (x+2 \)

One retailer charges \( \$ 1028 \) for a certain computer. A firm of tax accountants buys 7 of these computers. It makes a down payment of \( \$ 1100 \) and agrees to amortize the balance with monthly payments at \( 15 \% \) interest for 5 years. Prepare an amortization schedule showing the first four monthly payments for this loan. Write the equation that can be used to find the amount of each monthly payment. PMT \( =\frac{\mathrm{PV} \cdot \square}{1-(1+\square)} \) where PV \( =\square \) (Type integers or decimals. Simplify your answers.)

Use the distributive property to find the product. \[ \begin{aligned} 2 \cdot 9.35 & =2 \cdot(9+\square) \\ & =(2 \cdot \square)+(2 \cdot \square) \\ & =\square) \\ & =\end{aligned} \]