a piece of wire is 12s cm long.what will be the length of the side,if it is formed as 1)AN eqiulateral traingle
2)a square
Answers
Answer:
ANSWER.
Option [ b ] is correct answer.
EXPLANATION.
\begin{gathered} \sf : \implies \: { \underline{conditions \: of \: one - one \: and \: onto}} \\ \\ \sf : \implies \: \: one - one \: we \: must \: check \: f {}^{' } (x) > 0 \: \: or \: f {}^{' } (x) < 0 \: in \: given \: domain \\ \\ \sf : \implies \: in \: onto \: function \: range = codomain\end{gathered}
:⟹
conditionsofone−oneandonto
:⟹one−onewemustcheckf
′
(x)>0orf
′
(x)<0ingivendomain
:⟹inontofunctionrange=codomain
\begin{gathered} \sf : \implies \: f \ratio \: (0 , 3) \to \: (1 , 29) \\ \\ \sf : \implies \: f(x) = 2 {x}^{3} - 15 {x}^{2} + 36x + 1 \\ \\ \sf : \implies \: we \: can \: differentiate \: the \: equation \\ \\ \sf : \implies \: f {}^{ ' } (x) = 6 {x}^{2} - 30x + 36 \\ \\ \sf : \implies f {}^{ ' } (x) = 6( {x}^{2} - 5x + 6) \\ \\ \sf : \implies \: 6( {x}^{2} - 3x - 2x + 6) \end{gathered}
:⟹f:(0,3)→(1,29)
:⟹f(x)=2x
3
−15x
2
+36x+1
:⟹wecandifferentiatetheequation
:⟹f
′
(x)=6x
2
−30x+36
:⟹f
′
(x)=6(x
2
−5x+6)
:⟹6(x
2
−3x−2x+6)
\begin{gathered} \sf : \implies \: f {}^{ ' } (x) = 6(x - 2)( x - 3) \\ \\ \sf : \implies \: we \: can \: put \: the \: value \: in \:wavy \: curve \: method \\ \\ \sf : \implies \: zeroes \: of \: equation \: are =( 0,2,3) \\ \\ \sf: \implies \: the \: value \: given \: is \\ \\ \sf : \implies \:for \: given \: domain \: (0,3) \: \\ \\ \sf : \implies \: f(x) \: is \: increasing \: as \: well \: as \: decreasing \: \implies \: many \: one \: \end{gathered}
:⟹f
′
(x)=6(x−2)(x−3)
:⟹wecanputthevalueinwavycurvemethod
:⟹zeroesofequationare=(0,2,3)
:⟹thevaluegivenis
:⟹forgivendomain(0,3)
:⟹f(x)isincreasingaswellasdecreasing⟹manyone
\begin{gathered} \sf : \implies \: now \: put \: the \: value \: f {}^{'}(x) = 0 \\ \\ \sf : \implies \: 2(0 {}^{3} ) - 15( {0}^{2} ) + 36(0) + 1 \\ \\ \sf : \implies \: f(x) =1 \\ \\ \sf : \implies \: put \: f(2) \\ \\ \sf : \implies \: 2(2 {}^{3}) - 15(2 {}^{2} ) + 36(2) + 1 \\ \\ \sf : \implies \: 16 - 60 + 72 + 1 = 29 \\ \\ \sf : \implies \: f(2) = 29 \end{gathered}
:⟹nowputthevaluef
′
(x)=0
:⟹2(0
3
)−15(0
2
)+36(0)+1
:⟹f(x)=1
:⟹putf(2)
:⟹2(2
3
)−15(2
2
)+36(2)+1
:⟹16−60+72+1=29
:⟹f(2)=29
\begin{gathered} \sf : \implies \: f(3) \\ \\ \sf : \implies \: 2(3 {}^{3}) - 15(3 {}^{2} ) + 36(3) + 1 \\ \\ \sf : \implies \: 54 - 135 + 108 + 1 \\ \\ \sf : \implies \: f(3) = 28\end{gathered}
:⟹f(3)
:⟹2(3
3
)−15(3
2
)+36(3)+1
:⟹54−135+108+1
:⟹f(3)=28
\begin{gathered} \sf : \implies \: range \: = (1 , 29) \\ \\ \sf : \implies \: \green{{ \underline{function \: is \: onto \: but \: not \: one - one}}}\end{gathered}
:⟹range=(1,29)
:⟹
functionisontobutnotone−one
Answer:
Hot tea gets cool over time due to evaporation - hot molecules on the surface gets evaporated taking away heat with them.
2) Wet clothes dry in sun due to evaporation - the water in wet clothes takes heat energy from sun and gets evaporated.
3) Evaporation of perspiration from body - Sweat on our body evaporates taking away heat from our body
4) Drying of a mopped floor
5) Drying of wet hair after some time
6) drying up of water bodies like lakes and rivers
7) Evaporation of water from earthen pots
8) Evaporation of water sprinkled on ground or roof top
9) Evaporation of nail paint remover when applied on nails - acetone in nail paint remover takes heat from our body and evaporates.
10) Preparation of common salt from sea water by evaporation