The length of a curve <em>C</em> parameterized by a vector function <em>r</em><em>(t)</em> = <em>x(t)</em> i + <em>y(t)</em> j over an interval <em>a</em> ≤ <em>t</em> ≤ <em>b</em> is
In this case, we have
<em>x(t)</em> = exp(<em>t</em> ) + exp(-<em>t</em> ) ==> d<em>x</em>/d<em>t</em> = exp(<em>t</em> ) - exp(-<em>t</em> )
<em>y(t)</em> = 5 - 2<em>t</em> ==> d<em>y</em>/d<em>t</em> = -2
and [<em>a</em>, <em>b</em>] = [0, 2]. The length of the curve is then
Be yourself, think about it your crush is about to call you , you got this
You first multiply 6 and 8 to see how many people are put in the vans without rented a van. This would equal 48. You then subtract 48 from 59 to see how many people still need to be in a van. This would leave you with 11 people. Then you divide 8 from 11 to get 1 3/8. This means you need 2 vans to fit everyone.