Calories Burned by Joseph: Mathematics Exercise

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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?

-3.08 and 4.38 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?

-1.14𝑥 + 5.2 = 0 Signup and view all the answers

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

(a) Signup and view all the answers

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

-5 Signup and view all the answers

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

$1 - 14x$ Signup and view all the answers

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

$6x + y - 31 = 0$ Signup and view all the answers

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

8 Signup and view all the answers

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

-3.5 Signup and view all the answers

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

$1.2 \times 10^3$ 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)?

-254 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)?

4 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?

64 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?

-127n + 4 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?

[0, 3] 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?

[1, 3] Signup and view all the answers