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Throughout this question, you should use algebra to work out your answers, showing your working clearly. You may use a graph to check that your answers are correct, but it is not sufficient to read your results from a graph. (a) A straight line passes through the points (1,6) and (-2,-2). (i) Calculate the gradient of the line. Find the equation of the line. (ii) (iii) Find the r-intercept of the line. 1 (b) Does the line y =-=2+3 intersect with the line that you found in part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: 9x -3x+ 12 312 25 3 y = 12. 29

Throughout this question, you should use algebra to work out your answers, showing your working clearly. You may use a graph to check that your answers are correct, but it is not sufficient to read your results from a graph. (a) A straight line passes through the points (1,6) and (-2,-2). (i) Calculate the gradient of the line. Find the equation of the line. (ii) (iii) Find the r-intercept of the line. 1 (b) Does the line y =-=2+3 intersect with the line that you found in part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: 9x -3x+ 12 312 25 3 y = 12. 29

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Throughout this question, you should use algebra to work out your answers. showing your working clearly. You may use a graph to check that your answers are correct, but it is not sufficient to read your results from a graph. (a) A straight line passes through the points (1,6) and (-2,-2). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the r-intercept of the line. 1 (b) Does the line y part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: 9x - +3 intersect with the line that you found in 1 24 3 -3x+ y = 12. (d) Using a throwing stick, Dominic can throw his dog's ball across the park. Assume that the park is flat. The path of the ball can be modelled by the equation y = -0.02x²+x+2.6, where is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres). (i) Find the y-intercept of the parabola y = -0.022² +2+2.6 (the point at which the ball leaves the throwing stick). (ii) (1) By substituting 2-15 into the equation of the parabola, find the coordinates of the point where the line = 15 meets the parabola. (2) Using your answer to part (d) (ii) (1), explain whether the ball goes higher than a tree of height 4m that stands 15 m from Dominic and lies in the path of the ball. (iii) (1) Find the r-intercepts of the parabola. Give your answe decimal form, correct to two decimal places. aswers in (2) Assume that the ball lands on the ground. Use your answer from part (d) (iii) (1) to find the horizontal distance between where Dominic throws the ball, and where the ball first lands. (iv) Find the maximum height reached by the ball.
Transcribed Image Text:Throughout this question, you should use algebra to work out your answers. showing your working clearly. You may use a graph to check that your answers are correct, but it is not sufficient to read your results from a graph. (a) A straight line passes through the points (1,6) and (-2,-2). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the r-intercept of the line. 1 (b) Does the line y part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: 9x - +3 intersect with the line that you found in 1 24 3 -3x+ y = 12. (d) Using a throwing stick, Dominic can throw his dog's ball across the park. Assume that the park is flat. The path of the ball can be modelled by the equation y = -0.02x²+x+2.6, where is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres). (i) Find the y-intercept of the parabola y = -0.022² +2+2.6 (the point at which the ball leaves the throwing stick). (ii) (1) By substituting 2-15 into the equation of the parabola, find the coordinates of the point where the line = 15 meets the parabola. (2) Using your answer to part (d) (ii) (1), explain whether the ball goes higher than a tree of height 4m that stands 15 m from Dominic and lies in the path of the ball. (iii) (1) Find the r-intercepts of the parabola. Give your answe decimal form, correct to two decimal places. aswers in (2) Assume that the ball lands on the ground. Use your answer from part (d) (iii) (1) to find the horizontal distance between where Dominic throws the ball, and where the ball first lands. (iv) Find the maximum height reached by the ball.
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