Question-224081

Question Number 224081 by fantastic last updated on 18/Aug/25

Commented by fantastic last updated on 18/Aug/25

$${please}\:{tell}\:{me}\:{if}\:{i}\:{am}\:{right}\:{or}\:{wrong} \\ $$

Answered by Tokugami last updated on 18/Aug/25

vi) An object starts its journey from the point (5,0) and reaches the point (−7,0) in a semi−circular path. Then from there, it reaches point (3,0) in a semi−circular path and ends its journey. Find the total distance covered by the object. (5,0)→(−7,0) 5−(−7)=12→radius=6 length of semicircle with radius 6=6π (−7,0)→(3,0) 3−(−7)=10→radius=5 length of semicircle with radius 5=5π 6π+5π=11π ≈ ((242)/( 7)) vii) The diagonals of a rhombus are indicated by two coordinate axes. The coordinates of two consecutive corner points of the rhombus are (2,0) and (0,−4). Find the area of the rhombus. two remaining corner points: (−2,0) & (0,4) Area = (((4−(−4))×(2−(−2))/2) =((8×4)/2) =16

$$\left.\mathrm{vi}\right)\:\mathrm{An}\:\mathrm{object}\:\mathrm{starts}\:\mathrm{its}\:\mathrm{journey}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{5},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(−\mathrm{7},\mathrm{0}\right)\:\mathrm{in}\:\mathrm{a}\:\mathrm{semi}−\mathrm{circular}\:\mathrm{path}.\:\mathrm{Then} \\ $$$$\mathrm{from}\:\mathrm{there},\:\mathrm{it}\:\mathrm{reaches}\:\mathrm{point}\:\left(\mathrm{3},\mathrm{0}\right)\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{semi}−\mathrm{circular}\:\mathrm{path}\:\mathrm{and}\:\mathrm{ends}\:\mathrm{its}\: \\ $$$$\mathrm{journey}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{distance} \\ $$$$\mathrm{covered}\:\mathrm{by}\:\mathrm{the}\:\mathrm{object}. \\ $$$$\left(\mathrm{5},\mathrm{0}\right)\rightarrow\left(−\mathrm{7},\mathrm{0}\right) \\ $$$$\mathrm{5}−\left(−\mathrm{7}\right)=\mathrm{12}\rightarrow\mathrm{radius}=\mathrm{6} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{semicircle}\:\mathrm{with}\:\mathrm{radius}\:\mathrm{6}=\mathrm{6}\pi \\ $$$$\left(−\mathrm{7},\mathrm{0}\right)\rightarrow\left(\mathrm{3},\mathrm{0}\right) \\ $$$$\mathrm{3}−\left(−\mathrm{7}\right)=\mathrm{10}\rightarrow\mathrm{radius}=\mathrm{5} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{semicircle}\:\mathrm{with}\:\mathrm{radius}\:\mathrm{5}=\mathrm{5}\pi \\ $$$$\mathrm{6}\pi+\mathrm{5}\pi=\mathrm{11}\pi\:\approx\:\frac{\mathrm{242}}{\:\mathrm{7}} \\ $$$$\left.\mathrm{vii}\right)\:\mathrm{The}\:\mathrm{diagonals}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rhombus}\:\mathrm{are} \\ $$$$\mathrm{indicated}\:\mathrm{by}\:\mathrm{two}\:\mathrm{coordinate}\:\mathrm{axes}. \\ $$$$\mathrm{The}\:\mathrm{coordinates}\:\mathrm{of}\:\mathrm{two}\:\mathrm{consecutive} \\ $$$$\mathrm{corner}\:\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rhombus}\:\mathrm{are} \\ $$$$\left(\mathrm{2},\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{0},−\mathrm{4}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{rhombus}. \\ $$$$ \\ $$$$\mathrm{two}\:\mathrm{remaining}\:\mathrm{corner}\:\mathrm{points}: \\ $$$$\left(−\mathrm{2},\mathrm{0}\right)\:\&\:\left(\mathrm{0},\mathrm{4}\right) \\ $$$$\mathrm{Area}\:=\:\frac{\left(\mathrm{4}−\left(−\mathrm{4}\right)\right)×\left(\mathrm{2}−\left(−\mathrm{2}\right)\right.}{\mathrm{2}} \\ $$$$=\frac{\mathrm{8}×\mathrm{4}}{\mathrm{2}} \\ $$$$=\mathrm{16} \\ $$

Commented by fantastic last updated on 18/Aug/25

$${thank}\:{you}\:{very}\:{much} \\ $$

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