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Substitute x=3 into the function f(x).

Computer Science

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C

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here are the solutions to the problems:

50. If f(x)=2x2−1f(x) = 2x^2 - 1, then f(3)=f(3) =

  1. Substitute x=3x=3 into the function f(x)f(x).

    f(3)=2(3)2−1f(3) = 2(3)^2 - 1

  2. Calculate the square.

    f(3)=2(9)−1f(3) = 2(9) - 1

  3. Perform the multiplication.

    f(3)=18−1f(3) = 18 - 1

  4. Perform the subtraction.

    f(3)=17f(3) = 17

    The correct option is (C).

    C) 17\boxed{\text{C) } 17}

    51. What is the gradient of the straight line 2y=−3x−82y = -3x - 8?

  5. To find the gradient, rearrange the equation into the slope-intercept form y=mx+cy = mx + c, where mm is the gradient.

    2y=−3x−82y = -3x - 8

  6. Divide both sides of the equation by 2.

    y=−3x2−82y = \frac{-3x}{2} - \frac{8}{2} y=−32x−4y = -\frac{3}{2}x - 4

    The gradient mm is the coefficient of xx.

    m=−32m = -\frac{3}{2}

    The correct option is (B).

    B) −32\boxed{\text{B) } -\frac{3}{2}}

    52. What is the measure of ∠BAC\angle BAC?

  7. 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=ACAB = 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=BCBA = BC.

  8. Conclude the type of triangle.

    Since AB=ACAB = AC and BA=BCBA = BC, it follows that AB=AC=BCAB = AC = BC. Therefore, triangle ABC is an equilateral triangle.

  9. Determine the angle measure.

    In an equilateral triangle, all interior angles are equal to 60∘60^\circ.
    Thus, ∠BAC=60∘\angle BAC = 60^\circ.
    The correct option is (C).

    C) 60∘\boxed{\text{C) } 60^\circ}

    53. In the triangle, the value of xx is

  10. 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.

  11. 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∘40^\circ, so the other base angle must also be 40∘40^\circ.

  12. Use the sum of angles in a triangle.

    The sum of the interior angles in any triangle is 180∘180^\circ.

    x∘+40∘+40∘=180∘x^\circ + 40^\circ + 40^\circ = 180^\circ x∘+80∘=180∘x^\circ + 80^\circ = 180^\circ

  13. Solve for xx.

    x∘=180∘−80∘x^\circ = 180^\circ - 80^\circ x∘=100∘x^\circ = 100^\circ

    The correct option is (C).

    C) 100\boxed{\text{C) } 100}
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