Calories Burned by Joseph: Mathematics Exercise
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Questions and Answers

What is the model that represents the number of calories Joseph burns per minute after 6 minutes of training?

  • 2.6
  • 0.4 (correct)
  • 1.3
  • 3.1
  • How many times, in total, did Joseph's smart watch beep during the session?

  • 96 (correct)
  • 88
  • 112
  • 92
  • What does Jessica, the scientist, make a solution of?

  • Bicarbonate
  • Glucose
  • Acid (correct)
  • Uranium
  • In the equation ℎ(𝑥) = −1.14𝑥^2 + 5.2𝑥 − 0.13 = 0, what are the roots?

    <p>-3.08 and 4.38</p> Signup and view all the answers

    'What is Joseph's heart-rate at a maximum during the session?' is best answered by solving which equation?

    <p>-1.14𝑥 + 5.2 = 0</p> Signup and view all the answers

    'What is ℎ(6)?' is essential for solving which part of the given information?

    <p>(a)</p> Signup and view all the answers

    What is the value of $g(5)$?

    <p>-5</p> Signup and view all the answers

    What is the derivative $g'(x)$ of the function $g(x) = x - 7x^2 + x - 12$?

    <p>$1 - 14x$</p> Signup and view all the answers

    If $g(5) = 6$, what is the equation of the tangent to the curve $y=g(x)$ at $x=5$?

    <p>$6x + y - 31 = 0$</p> Signup and view all the answers

    From the given graph, at what value of $x$ is the derivative $u'(x)$ negative?

    <p>8</p> Signup and view all the answers

    Estimate the value of $u'(4)$ using the tangent drawn at point (4, 2) on the graph.

    <p>-3.5</p> Signup and view all the answers

    Express $1200$ in scientific notation form $a \times 10^n$ where $1 \leq a < 10$.

    <p>$1.2 \times 10^3$</p> Signup and view all the answers

    What is the value of the first term (T) in an arithmetic sequence given by the expression T = -254 + (n - 1)(4)?

    <p>-254</p> Signup and view all the answers

    What is the common difference in the arithmetic sequence where the nth term is T = -254 + (n - 1)(4)?

    <p>4</p> Signup and view all the answers

    For the equation -254 + (n - 1)(4) = 0, what is the smallest value of n that satisfies this equation?

    <p>64</p> Signup and view all the answers

    In the arithmetic sequence given by T = -254 + (n - 1)(4), what is the sum of the first n terms if n is a natural number?

    <p>-127n + 4</p> Signup and view all the answers

    Based on the graphs provided for k(x) and m(x), what is the range of values for x where k(x) is less than m(x) for 0 ≤ x ≤ 5?

    <p>[0, 3]</p> Signup and view all the answers

    For 0 ≤ x ≤ 5, what are the two values of x for which m(x) = 0 based on the given graphs?

    <p>[1, 3]</p> Signup and view all the answers

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