Write in surd form
2 answers:
<h2>Answer: 169 √(13)</h2>
Step-by-step explanation:
We can rewrite in a form that makes it easier to see:
13^{\frac{5}{2} } = √[(13)⁵]
Now, we want to factorise and rewrite (13)⁵ so that one of the factors is a perfect square
13⁵ = 13⁴ × 13 (where 13⁴ is a perfect square)
⇒ √[(13)⁵] = √[ 13⁴ × 13] <em>[separate each term on LHS]</em>
= √(13⁴) × √(13) <em> [square root the perfect square]</em>
= 13² √(13) <em> [simplify]</em>
= 169 √(13)
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The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.
To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.
By definition of absolute value,
Over this particular integration interval,
• sin(<em>t</em> ) ≥ 0 for 1 ≤ <em>t</em> < <em>π</em>, and
• sin(<em>t</em> ) < 0 for <em>π</em> < <em>t</em> ≤ 5
so you end up splitting the integral at <em>t</em> = <em>π</em> as
Now compute the distance:
making B the correct answer.