Straight Lines‚ Pair of Lines & Circles A straight line through the point A 3‚ 4 is such that its intercept between the axes is bisected at A . It’s equation is 1. (a) 4 x 3 y 24 Ans: a (b) 3x 4 y 25 (c) x y 7 (d) 3x 4 y 7 0 Sol: By formula required equation is given by x y 2 4 x 3 y 24 3 4 2. The equation of the line which is the perpendicular bisector of the line joining the points 3‚ 5 and 9‚3 is (a) 4 x 3 y 14 0 Ans: d Sol: A 3‚
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Number of meals consumed per day (X) child weight (Y) X² Y² XY Ahmad 11 8 121 64 88 Ali 16 11 256 121 176 Osama 12 9 144 81 108 Husien 19 13 361 169 247 Total 58 41 882 435 619 a. Determine the simple linear regression equation. b. Determine the correlation coefficient. Interpret it in words. c. What is the expected child weight if the number of meals increased by 2 meals per day? Q2. A hospital supervisor wishes to find the relationship between the number
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point… you must be The slope of a d-t graph always equals moving at a constant positive velocity! the velocity of the object at that time. ● A constant positive velocity is shown on a d-t graph as a straight line that slopes upwards. It is a linear relationship. ● In fact‚ if you found the slope of the line in this section‚ it will be the velocity that you were running at. rise d
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no longer a parabola. Now we will look at how the (b) factor changes the parabola‚ below is the origional graph from the top of the paper except the red line represents the same parabola with a (b) added onto it. The original equation was Y=x^2(blue line) and the new equation is Y=x^2+x(red line). The change is moving the vertex of the parabola left ½ and down ¼ but the shape of the parabola it’s self is unchanged. Here are some other examples of changing (b) in a parabola with a steady (a) As seen
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In the science Isa the materials we can take in is the Crn notes‚ our table we drew as well as the graph we drew. Question 1) Do your results agree with your hypothesis? Yes our results do agree with the hypothesis because as soon as the weights were lifted the muscles began to fatigue very rapidly‚ an example of when this occurred is once the 1kg weight was lifted it took … amount of seconds to fatigue however as soon as the 5kg weight was lifted we saw the muscles fatigued extremely quickly
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monthly payments 2 d) Simultaneous equations: ( solving by elimination) Deposit = $350 Total monthly payments = 10 months x 120 By multiplying the second equation by 3‚ we get: = $1‚200 Total hire purchase price = 350 + 1200 = $1‚550 2x +3y = 9 9x – 3y = 24 By adding both equation we get: 11x = 33 so (x = 3) Q1.c (ii) Amount saved if laptop is purchased for cash of $1‚299 = 1‚550 – 1‚299 By substituting (x=3) into the first equation we get: = $251 2(3)+3y = 9
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direct proportion. The equation for the trend line is Y = 20.788 X - 0.0093 ; R ² = 0.9675. This equation will be used to calculate the unknown concentration of Methylene Blue solution. Figure 2: Standard curve of Average light absorbance by ten different concentration of Methlene Blue. The data is collected from all the groups in the class. All the points in the graph represent the means of all the groups. The figure shows a direct proportion. Its equation for trend line is Y = 23
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Q.1. What is a linear programming problem ? Discuss the steps and role of linear programming is solving management problems. Discuss and describe the role of liner programming in managerial decision-making bringing out limitations‚ if any. Ans : Linear Programming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of given criterion of optimality. The usefulness of linear programming as a tool for optimal decision-making
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The formula used to write an inequality is: y=mx+b m=y2-y1/x2-x1 this tells me that my slope is: y=mx+b y=x+330 Slope intercept form (1)y=(1)+330(1) multiply both sides by 1 Y=-3x+330 Y+3x=3x+3≤330 add both sides by 3 3x+y≤330 linear inequality for my line The next question asked is will the truck hold 71 refrigerators and the 118 TVs. In order to answer the question I need to determine if points (71‚ 118) are within the shaded part of my graph. X=71 y=118 3(71)+118≤330
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polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax + b‚ zero of the polynomial will be given by the expression (-b/a). 5. The number of real zeros of the polynomial is the number of times its graph touches or intersects x axis. 6. 7. 8. 9. 10. A polynomial p(x) of degree n will have atmost n real zeroes A linear polynomial has atmost one real zero. A quadratic polynomial has atmost two real zeroes. A cubic
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