Given below are two statements, one labelled as Assertion (A) and the other as Reason (R).\n **Assertion (A):** High jumpers are provided with cushioned beds or sand pits to land on after their jump to prevent severe injuries.\n **Reason (R):** The cushioned bed increases the duration of the impact, which reduces the rate of change of momentum and consequently decreases the average force exerted on the athlete's body.\n Choose the correct option:
Options:
- A: Both A and R are true and R is the correct explanation of A.
- B: Both A and R are true but R is NOT the correct explanation of A.
- C: A is true but R is false.
- D: A is false but R is true.
Related Practice Questions:
- Let $S_1$ and $S_2$ be two disjoint, non-empty convex sets in $\mathbb{R}^n$. Under which of the following conditions is there guaranteed to exist a hyperplane that strictly separates $S_1$ and $S_2$?
- Let the primal linear programming problem be: Maximize $Z = c^T x$ subject to $Ax \le b, x \ge 0$. If this primal problem has an unbounded optimal objective value, then which of the following statements is always true regarding its dual problem?
- Let $S = \{(x, y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 9\}$ be a convex set in $\mathbb{R}^2$. The set of all extreme points of $S$ is given by:
- In a linear programming problem with $3$ independent equality constraints and $5$ variables (including slack/surplus variables), what is the maximum possible number of basic solutions?