This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
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You're on a roll — here are the solutions to the problems: 50. If f(x) = 2x^2 - 1, then f(3) = Step 1: Substitute x=3 into the function f(x). f(3) = 2(3)^2 - 1 Step 2: Calculate the square. f(3) = 2(9) - 1 Step 3: Perform the multiplication. f(3) = 18 - 1 Step 4: Perform the subtraction. f(3) = 17 The correct option is (C). C) 17 51. What is the gradient of the straight line 2y = -3x - 8? Step 1: To find the gradient, rearrange the equation into the slope-intercept form y = mx + c, where m is the gradient. 2y = -3x - 8 Step 2: Divide both sides of the equation by 2. y = (-3x)/(2) - (8)/(2) y = -(3)/(2)x - 4 The gradient m is the coefficient of x. m = -(3)/(2) The correct option is (B). B) -(3)/(2) 52. What is the measure of BAC? Step 1: Analyze the construction description. "With centre A, an arc BC is drawn." This means that the distance from A to B is equal to the distance from A to C. So, AB = AC. "With centre B, and the same radius, the arc PCQ is drawn." This means the distance from B to A is equal to the distance from B to C. So, BA = BC. Step 2: Conclude the type of triangle. Since AB = AC and BA = BC, it follows that AB = AC = BC. Therefore, triangle ABC is an equilateral triangle. Step 3: Determine the angle measure. In an equilateral triangle, all interior angles are equal to 60^. Thus, BAC = 60^. The correct option is (C). C) 60^ 53. In the triangle, the value of x is Step 1: Identify the properties of the triangle. The markings on two sides of the triangle indicate that it is an isosceles triangle, meaning those two sides are equal in length. Step 2: Apply the property of isosceles triangles. In an isosceles triangle, the angles opposite the equal sides are also equal. One of the base angles is given as 40^, so the other base angle must also be 40^. Step 3: Use the sum of angles in a triangle. The sum of the interior angles in any triangle is 180^. x^ + 40^ + 40^ = 180^ x^ + 80^ = 180^ Step 4: Solve for x. x^ = 180^ - 80^ x^ = 100^ The correct option is (C). C) 100 What's next?