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Question Number 14921 Answers: 1 Comments: 2

A car travelling at 36 km/h due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?

$$\mathrm{A}\:\mathrm{car}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{36}\:\mathrm{km}/\mathrm{h}\:\mathrm{due}\:\mathrm{North} \\ $$$$\mathrm{turns}\:\mathrm{West}\:\mathrm{in}\:\mathrm{5}\:\mathrm{seconds}\:\mathrm{and}\:\mathrm{maintains} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{speed}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{car}? \\ $$

Question Number 14920 Answers: 1 Comments: 0

A swimmer crosses a flowing river of width d to and fro in time t_1 . The time taken to cover the same distance up and down the stream is t_2 . If t_3 is the time the swimmer would take to swim a distance 2d in still water, then prove that t_1 ^2 = t_2 t_3 .

$$\mathrm{A}\:\mathrm{swimmer}\:\mathrm{crosses}\:\mathrm{a}\:\mathrm{flowing}\:\mathrm{river}\:\mathrm{of} \\ $$$$\mathrm{width}\:{d}\:\mathrm{to}\:\mathrm{and}\:\mathrm{fro}\:\mathrm{in}\:\mathrm{time}\:{t}_{\mathrm{1}} .\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:\mathrm{the}\:\mathrm{same}\:\mathrm{distance}\:\mathrm{up} \\ $$$$\mathrm{and}\:\mathrm{down}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{is}\:{t}_{\mathrm{2}} .\:\mathrm{If}\:{t}_{\mathrm{3}} \:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{time}\:\mathrm{the}\:\mathrm{swimmer}\:\mathrm{would}\:\mathrm{take}\:\mathrm{to}\:\mathrm{swim} \\ $$$$\mathrm{a}\:\mathrm{distance}\:\mathrm{2}{d}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{t}_{\mathrm{1}} ^{\mathrm{2}} \:=\:{t}_{\mathrm{2}} {t}_{\mathrm{3}} . \\ $$

Question Number 14905 Answers: 0 Comments: 5

Question Number 14863 Answers: 1 Comments: 8

Question Number 14853 Answers: 1 Comments: 0

Solve for x 3^(2x) = 18x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{3}^{\mathrm{2x}} \:=\:\mathrm{18x} \\ $$

Question Number 14821 Answers: 1 Comments: 0

A room has dimensions 3 m × 4 m × 5 m. A fly starting at one corner ends up at the diametrically opposite corner. If the fly were to walks, what is the length of the shortest path it can take?

$$\mathrm{A}\:\mathrm{room}\:\mathrm{has}\:\mathrm{dimensions}\:\mathrm{3}\:\mathrm{m}\:×\:\mathrm{4}\:\mathrm{m}\:×\:\mathrm{5}\:\mathrm{m}. \\ $$$$\mathrm{A}\:\mathrm{fly}\:\mathrm{starting}\:\mathrm{at}\:\mathrm{one}\:\mathrm{corner}\:\mathrm{ends}\:\mathrm{up}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{diametrically}\:\mathrm{opposite}\:\mathrm{corner}.\:\mathrm{If} \\ $$$$\mathrm{the}\:\mathrm{fly}\:\mathrm{were}\:\mathrm{to}\:\mathrm{walks},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{path}\:\mathrm{it}\:\mathrm{can}\:\mathrm{take}? \\ $$

Question Number 14816 Answers: 1 Comments: 0

Question Number 14811 Answers: 1 Comments: 0

why (√x^2 )=∣x∣ ?

$${why}\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} }=\mid{x}\mid\:\:\:\:?\: \\ $$

Question Number 14810 Answers: 0 Comments: 0

7 real numbers are given in the interval (1, 13). Prove that atleast 3 of them are the lengths of a triangle′s sides.

$$\mathrm{7}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{given}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left(\mathrm{1},\:\mathrm{13}\right).\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{atleast}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}'\mathrm{s}\:\mathrm{sides}. \\ $$

Question Number 14809 Answers: 1 Comments: 2

Let ABC be an acute triangle. Find the positions of the points M, N, P on the sides BC, CA, AB, respectively, such that the perimeter of the triangle MNP is minimal.

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{an}\:\mathrm{acute}\:\mathrm{triangle}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{positions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{points}\:{M},\:{N},\:{P}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA},\:{AB},\:\mathrm{respectively}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle} \\ $$$${MNP}\:\mathrm{is}\:\mathrm{minimal}. \\ $$

Question Number 14807 Answers: 0 Comments: 0

Prove that the medians of a given triangle can form a triangle.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{medians}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{triangle}\:\mathrm{can}\:\mathrm{form}\:\mathrm{a}\:\mathrm{triangle}. \\ $$

Question Number 14797 Answers: 1 Comments: 12