Everything Maths Grade 12

8.3 CHAPTER 8. LINEAR PROGRAMMING which has been drawn in Figure 8.2. Level linescorresponding to f (x,y) =− 10 or y = x 2 + 5 f ...

CHAPTER 8. LINEAR PROGRAMMING 8.3 The feasible region is always a polygon. Solutions occur at vertices of the feasible region. ...

8.3 CHAPTER 8. LINEAR PROGRAMMING Step 1 : Identify the decision variables Let the number of kettles be x and the number of toas ...

CHAPTER 8. LINEAR PROGRAMMING 8.3 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 10 0 x y A B Step 7 : Calculate cost ...

8.3 CHAPTER 8. LINEAR PROGRAMMING go through are: bodywork and engine work. The factory cannot operate for less than 360 hours ...

CHAPTER 8. LINEAR PROGRAMMING 8.3 Step 3 : Profit equation P = 1 200x + 400y Step 4 : Maximum profit By moving the search line u ...

8.3 CHAPTER 8. LINEAR PROGRAMMING A small cell phone company makes two typesof cell phones: Easyhear and Longtalk. Production f ...

Geometry 9 9.1 Introduction In previous years, you learned about the geometry of points, lines and various polygons, made upfrom ...

9.2 CHAPTER 9. GEOMETRY � A � B O P ar c chord tangent diameter radius segment Figure 9.1: Parts of a circle B C A Figure 9.2: A ...

CHAPTER 9. GEOMETRY 9.2 Proof: � A B O P Consider a circle, with centre O. Draw a chord AB and draw a perpendicular line from th ...

9.2 CHAPTER 9. GEOMETRY AP = PB (given) OA = OB (radii) OP is common to both triangles. ∴�OAP≡�OBP (SSS). OPAˆ = OPBˆ OPAˆ +OP ...

CHAPTER 9. GEOMETRY 9.2 Exercise 9 - 1 Find the value of x: 1. O x 5 P Q R PR=8 2. O 4 P Q R PR=6 x 3. O x 10 P Q R PR=8 4. O x ...

9.2 CHAPTER 9. GEOMETRY Theorem 4. The angle subtended by an arc at the centre of a circle is double thesize of the angle subten ...

CHAPTER 9. GEOMETRY 9.2 Exercise 9 - 2 Find the angles (a to f ) indicated in each diagram: � � � � � � J H K J J J J J H H H H ...

9.2 CHAPTER 9. GEOMETRY Consider a circle, with centre O. Draw a chord AB. Select any points P and Q on the circumference of the ...

CHAPTER 9. GEOMETRY 9.2 1. 2. 3. 4. 5. 6. � A B C D E F G H I J K L M N O P Q R S T U V W X Y Z O 21 ◦ a 15 ◦ b 24 ◦ c d 17 ◦ 45 ...

9.2 CHAPTER 9. GEOMETRY O� A B P Q 1 2 Consider a circle, with centre O. Draw a cyclic quadrilateral ABPQ. Draw AO and PO. The a ...

CHAPTER 9. GEOMETRY 9.2 ∴ the assumption that thecircle does not pass through P , must be false, and A, B, P and Q lie on the ci ...

9.2 CHAPTER 9. GEOMETRY � A B O P Consider a circle, with centre O. Choose a point P outside the circle. Drawtwo tangents to the ...

CHAPTER 9. GEOMETRY 9.2 1. 2. 3. 4. � � R Q S 3 cm � � A B C D E F G H I J K L M N O P AE = 5 cm AC = 8 cm a CE = 9 cm b c � � � ...