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Question Number 202154 Answers: 3 Comments: 1

f(xy+1)= f(x)f(y)−2f(y)−x+5

$$\:\: \mathrm{f}\left(\mathrm{xy}+\mathrm{1}\right)=\: \mathrm{f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{y}\right)−\mathrm{2f}\left(\mathrm{y}\right)−\mathrm{x}+\mathrm{5}\: \\ $$$$\:\:\: \\ $$

Question Number 202153 Answers: 1 Comments: 0

Question Number 202146 Answers: 0 Comments: 1

There are three children in a family. Two of the children have blood group III, and one has blood group I. If the father of the children has blood type III, what is the probability that the mother will also have blood type III ?

$$ \\ $$There are three children in a family. Two of the children have blood group III, and one has blood group I. If the father of the children has blood type III, what is the probability that the mother will also have blood type III ?

Question Number 202143 Answers: 0 Comments: 5

find x in the interval 0°<x<360° if f(x)= 6sinx is −12

$$\:{find}\:{x}\:{in}\:{the}\:{interval}\:\:\mathrm{0}°<{x}<\mathrm{360}°\:{if} \\ $$$$\:\:{f}\left({x}\right)=\:\mathrm{6}{sinx}\:{is}\:−\mathrm{12} \\ $$

Question Number 202129 Answers: 1 Comments: 0

If p = 9999 then ((4p^3 − p)/((2p + 1)(6p − 3))) = ?

$$\mathrm{If}\:{p}\:=\:\mathrm{9999}\:\mathrm{then}\:\frac{\mathrm{4}{p}^{\mathrm{3}} \:−\:{p}}{\left(\mathrm{2}{p}\:+\:\mathrm{1}\right)\left(\mathrm{6}{p}\:−\:\mathrm{3}\right)}\:=\:? \\ $$

Question Number 202128 Answers: 0 Comments: 0

Question Number 202127 Answers: 1 Comments: 0

Question Number 202125 Answers: 1 Comments: 0

∫ ((sin(3x))/(1+sin^3 x))dx

$$\int\:\frac{\boldsymbol{{sin}}\left(\mathrm{3}\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$

Question Number 202123 Answers: 2 Comments: 0

(1/(1×3)) + (1/(3×5)) + (1/(5×7)) + ...............∞ = ?

$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{7}}\:+\:...............\infty\:=\:? \\ $$

Question Number 202120 Answers: 2 Comments: 0

If α and β are the roots of ax^2 + bx + c = 0. If ((1 − α)/α) and ((1 − β)/β) are the roots of a_1 x^2 + b_1 x + c_1 = 0. If (b_1 /a_1 ) = k + (b/c) then k = ?

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}.\:\mathrm{If}\:\:\frac{\mathrm{1}\:−\:\alpha}{\alpha}\:\mathrm{and}\:\frac{\mathrm{1}\:−\:\beta}{\beta}\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{a}_{\mathrm{1}} {x}^{\mathrm{2}} \:+\:{b}_{\mathrm{1}} {x}\:+\:{c}_{\mathrm{1}} \:=\:\mathrm{0}.\:\mathrm{If} \\ $$$$\frac{{b}_{\mathrm{1}} }{{a}_{\mathrm{1}} }\:=\:{k}\:+\:\frac{{b}}{{c}}\:\mathrm{then}\:{k}\:=\:? \\ $$

Question Number 202117 Answers: 0 Comments: 0

Question Number 202116 Answers: 2 Comments: 0

(√3^x ) +1=2^x find x

$$\sqrt{\mathrm{3}^{\boldsymbol{{x}}} }\:+\mathrm{1}=\mathrm{2}^{\boldsymbol{{x}}} \:\:\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$

Question Number 202114 Answers: 2 Comments: 0

If α and β are the roots of ax^2 + bx + c = 0 and α + k and β + k are the roots of lx^2 + mx + n = 0 then prove that k = (1/2)((b/a) − (m/l)).

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:{k}\:\mathrm{and}\:\beta\:+\:{k}\:\:\mathrm{are}\: \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{lx}^{\mathrm{2}} \:+\:{mx}\:+\:{n}\:=\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{k}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{b}}{{a}}\:−\:\frac{{m}}{{l}}\right). \\ $$

Question Number 202109 Answers: 1 Comments: 0

How many different three-digit numbers a satisfy the condition GCD(a;18)>=2 ?

$$ \\ $$How many different three-digit numbers a satisfy the condition GCD(a;18)>=2 ?

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 = ?

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

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