Question 1

Please help with full workings

Question 2

a)

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 4}}\quad ,&{{ 6}})\quad % (c,d) B&({{ 28}}\quad ,&{{ 11}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{11-6}{28-4}\implies \cfrac{5}{24}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=\cfrac{5}{24}(x-4)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-6=\cfrac{5}{24}x-\cfrac{5}{6}\implies y=\cfrac{5}{24}x-\cfrac{5}{6}+6 \\\\\\ y=\cfrac{5}{24}x+\cfrac{31}{6}$

b)

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 4}}\quad ,&{{ 6}})\quad % (c,d) B&({{ 28}}\quad ,&{{ 11}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=√((28-4)^2+(11-6)^2)\implies AB=√(24^2+5^2)\implies AB=√(601)$

c)

well, the speed of the ship, the ship took two hours to cover the distance AB, thus the speed is length/time

$\bf \cfrac{AB\ kms}{2hours}\implies \cfrac{√(601)\ kms}{2\ hrs}\approx 12.25765\ (kms)/(hrs)$

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