Question 319 marks Throughout this question, you should use algebra to work out

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Question 319 marks Throughout this question, you should use algebra to work out your answers. 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 (-3,4) and (2,2). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (ii) Find the z-intercept of the line. (b) Does the point (4,4) lie on 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: -2 +3y 1. (d) A cannon enthusiast is planning a display. When the cannon is at a given angle, the trajectory of the cannon ball can be modelled by the equation y-0.001222 +0.4625z +5, where z is the horizontal distance of the cannon ball from the cannon, and y is the vertical distance of the ball above the ground (both measured in metres). Find the y-intercept of the parabola y-0.001222 + 0.4625z+5 (the height at which the cannon ball leaves the cannon). (i) (ü) (1) By substituting a 100 into the equation of the parabola, find -100 meets the (2) Using your answer to part (d)(i) (1), explain whether the ball the coordinates of the point where the line parabola. would go higher than a tree of height 30 m that stands 100 m from the planned position of the cannon and lies in the path of the cannon ball. (ii) (1) Find the r-intercepts of the parabola. Give your answers in decimal form, correct to two significant figures. (2) Assume that the cannon ball lands on the ground. Use your answers from part (d)(i) and part (d)(ii)(1) to find the horizontal distance between the cannon and where the cannon ball first lands.

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first complete question and two next questions according to chegg policy in case of multiple questions.

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