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Question Number 202104 Answers: 2 Comments: 2

Question Number 202102 Answers: 2 Comments: 0

If x = 3 + 2(√2) then ((x^6 + x^4 + x^2 + 1)/x^3 ) = ?

$$\mathrm{If}\:{x}\:=\:\mathrm{3}\:+\:\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{then}\:\frac{{x}^{\mathrm{6}} \:+\:{x}^{\mathrm{4}} \:+\:{x}^{\mathrm{2}} \:+\:\mathrm{1}}{{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 202100 Answers: 1 Comments: 0

Question Number 202094 Answers: 0 Comments: 2

A computer systerm has a memory leak issue causing its usage to increase over time. the rate of memory usage growth is directly proportional to the difference between the current memory usage and the systerms maximum memory capacity. Write one ODE and one PDE that models the memory usage growth.

$$\:{A}\:{computer}\:{systerm}\:{has}\:{a}\:{memory}\: \\ $$$$\:\:{leak}\:{issue}\:{causing}\:{its}\:{usage}\:{to} \\ $$$$\:\:{increase}\:{over}\:{time}.\:{the}\:{rate}\:{of}\: \\ $$$$\:\:{memory}\:{usage}\:{growth}\:{is}\:{directly}\: \\ $$$$\:\:{proportional}\:{to}\:{the}\:{difference}\: \\ $$$$\:\:{between}\:{the}\:{current}\:{memory}\:{usage}\: \\ $$$$\:{and}\:{the}\:{systerms}\:{maximum}\:{memory} \\ $$$$\:\:{capacity}.\:{Write}\:{one}\:{ODE}\:{and}\:{one}\: \\ $$$$\:\:{PDE}\:{that}\:{models}\:{the}\:{memory}\:{usage} \\ $$$$\:\:{growth}. \\ $$

Question Number 202093 Answers: 1 Comments: 2

Question Number 202086 Answers: 1 Comments: 0

There are two possible routes from Zindhi to Katifa. One route is through Zindhi/Chadler expressway which is 100km and the other is through Adfeti and Ngonu covering a distance of 80km. A motorist going through the expressway can travel 10km/h faster than the one going through Adfeti and Ngonu, and arrive Katifa 5 minutes earlier as well. What is the time spent on the journey to Katifa by the motorist travelling through the expressway.

$${There}\:{are}\:{two}\:{possible}\:{routes}\:{from} \\ $$$${Zindhi}\:{to}\:{Katifa}.\:{One}\:{route}\:{is}\:{through} \\ $$$${Zindhi}/{Chadler}\:{expressway}\:{which}\:{is} \\ $$$$\mathrm{100}{km}\:{and}\:{the}\:{other}\:{is}\:{through}\:{Adfeti}\:{and} \\ $$$${Ngonu}\:{covering}\:{a}\:{distance}\:{of}\:\mathrm{80}{km}.\:{A} \\ $$$${motorist}\:{going}\:{through}\:{the}\:{expressway} \\ $$$${can}\:{travel}\:\mathrm{10}{km}/{h}\:{faster}\:{than}\:{the}\:{one} \\ $$$${going}\:{through}\:{Adfeti}\:{and}\:{Ngonu},\:{and} \\ $$$${arrive}\:{Katifa}\:\mathrm{5}\:{minutes}\:{earlier}\:{as}\:{well}. \\ $$$${What}\:{is}\:{the}\:{time}\:{spent}\:{on}\:{the}\:{journey} \\ $$$${to}\:{Katifa}\:{by}\:{the}\:{motorist}\:{travelling} \\ $$$${through}\:{the}\:{expressway}. \\ $$

Question Number 202084 Answers: 0 Comments: 0

Question Number 202082 Answers: 2 Comments: 0

Question Number 202079 Answers: 1 Comments: 0

A man travelled from town A to B, a distance of 360km. He left A one hour later than he had planned so he decided to drive at 5km/h faster than his normal speed, in order to reach B on schedule. If he arrived B at exactly the scheduled time, find the normal speed.

$${A}\:{man}\:{travelled}\:{from}\:{town}\:{A}\:{to}\:{B},\:{a} \\ $$$${distance}\:{of}\:\mathrm{360}{km}.\:{He}\:{left}\:{A}\:{one}\:{hour} \\ $$$${later}\:{than}\:{he}\:{had}\:{planned}\:{so}\:{he}\:{decided} \\ $$$${to}\:{drive}\:{at}\:\mathrm{5}{km}/{h}\:{faster}\:{than}\:{his} \\ $$$${normal}\:{speed},\:{in}\:{order}\:{to}\:{reach}\:{B}\:{on} \\ $$$${schedule}.\:{If}\:{he}\:{arrived}\:{B}\:{at}\:{exactly}\:{the} \\ $$$${scheduled}\:{time},\:{find}\:{the}\:{normal}\:{speed}. \\ $$

Question Number 202058 Answers: 1 Comments: 1

Solve by computer programming a, b & c are Prime numbers. And they are in AP and d is common difference Example (a, b, c, d) = (3, 5, 7, 2) Just Next Set(a, b, c, d) = ?

$$\mathrm{Solve}\:\mathrm{by}\:\mathrm{computer}\:\mathrm{programming} \\ $$$${a},\:{b}\:\&\:{c}\:{are}\:{Prime}\:{numbers}.\:\mathrm{And}\:\mathrm{they} \\ $$$$\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:\mathrm{d}\:\mathrm{is}\:\mathrm{common}\:\mathrm{difference} \\ $$$$\mathrm{Example}\:\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:\left(\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\mathrm{Just}\:\mathrm{Next}\:\mathrm{Set}\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:? \\ $$

Question Number 202056 Answers: 0 Comments: 9

Question Number 202044 Answers: 2 Comments: 1

If a = 9999999998000000001 Find A = (((√a) + 1))^(1/9) → A = ?

$$\mathrm{If} \\ $$$$\mathrm{a}\:=\:\mathrm{9999999998000000001} \\ $$$$\mathrm{Find} \\ $$$$\mathrm{A}\:=\:\sqrt[{\mathrm{9}}]{\sqrt{\mathrm{a}}\:+\:\mathrm{1}}\:\:\:\rightarrow\:\:\:\mathrm{A}\:=\:? \\ $$

Question Number 202041 Answers: 1 Comments: 0

Simplify: (((√2) − sinα − cosα)/(sinα − cosα))

$$\mathrm{Simplify}:\:\:\:\frac{\sqrt{\mathrm{2}}\:−\:\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha}{\mathrm{sin}\alpha\:−\:\mathrm{cos}\alpha} \\ $$

Question Number 202034 Answers: 1 Comments: 0

Question Number 202039 Answers: 1 Comments: 0

Question Number 202037 Answers: 1 Comments: 0

A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

$$ \\ $$A board has 2, 4, and 6 written on it. One repeatedly chooses values (not necessarily different) for x, y, and z from the board, and writes xyz + xy + yz + zx + x + y + z if and only if those numbers are not already on the board and are also less than or equals 2013. The person repeats this process until no more numbers can be written. How many numbers will be written at the end of this process?

Question Number 202035 Answers: 0 Comments: 0

Question Number 202019 Answers: 3 Comments: 0

If α and β are the roots of the ax^2 + 2bx + c = 0 and α + δ and β + δ are the roots of Ax^2 + 2Bx + C = 0 for some constant δ then prove that ((b^2 − ac)/a^2 ) = ((B^2 − AC)/A^2 ) .

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$${ax}^{\mathrm{2}} \:+\:\mathrm{2}{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:\delta\:\mathrm{and}\:\beta\:+\:\delta\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{Ax}^{\mathrm{2}} \:+\:\mathrm{2}{Bx}\:+\:{C}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{some}\: \\ $$$$\mathrm{constant}\:\delta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{b}^{\mathrm{2}} \:−\:{ac}}{{a}^{\mathrm{2}} }\:=\:\frac{{B}^{\mathrm{2}} \:−\:{AC}}{{A}^{\mathrm{2}} }\:. \\ $$

Question Number 202017 Answers: 3 Comments: 0