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AllQuestion and Answers: Page 203

Question Number 202184 Answers: 2 Comments: 0

with f(x)=x^2 +12x+30 and x∈R solve f(f(f(f(f(x)))))=0

$${with}\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{30}\:{and}\:{x}\in{R} \\ $$$${solve}\:{f}\left({f}\left({f}\left({f}\left({f}\left({x}\right)\right)\right)\right)\right)=\mathrm{0} \\ $$

Question Number 202183 Answers: 1 Comments: 1

what is (√2) over 2

$$\boldsymbol{{what}}\:\boldsymbol{{is}}\:\sqrt{\mathrm{2}}\:\boldsymbol{{over}}\:\mathrm{2} \\ $$

Question Number 202562 Answers: 2 Comments: 0

Question Number 202172 Answers: 1 Comments: 0

If log_(12) 18 = A and log_(24) 54 = B then prove that AB + 5(A − B) = 1.

$$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{18}\:=\:\mathrm{A}\:\mathrm{and}\:\mathrm{log}_{\mathrm{24}} \mathrm{54}\:=\:\mathrm{B}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{AB}\:+\:\mathrm{5}\left(\mathrm{A}\:−\:\mathrm{B}\right)\:=\:\mathrm{1}. \\ $$

Question Number 202170 Answers: 1 Comments: 0

Question Number 202167 Answers: 2 Comments: 0

∫^1 _0 ∫^1 _x sin(y^2 )dydx = ¿

$$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \underset{{x}} {\int}^{\mathrm{1}} {sin}\left({y}^{\mathrm{2}} \right){dydx}\:=\:¿ \\ $$

Question Number 202161 Answers: 2 Comments: 0

Question Number 202160 Answers: 1 Comments: 0

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.

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

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