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Question Number 175315 Answers: 0 Comments: 0

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simplfy sinh(log2)

$$\mathrm{simplfy} \\ $$$$\:\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{log}}\mathrm{2}\right) \\ $$

Question Number 175284 Answers: 1 Comments: 0

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A biology class at central high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014. Find the equations represents the class model of the population over time?

$$\mathrm{A}\:\mathrm{biology}\:\:\mathrm{class}\:\mathrm{at}\:\mathrm{central}\:\:\mathrm{high}\:\:\mathrm{school} \\ $$$$\mathrm{predicted}\:\:\mathrm{that}\:\:\mathrm{a}\:\:\mathrm{local}\:\:\mathrm{population}\:\:\mathrm{of}\:\:\:\mathrm{animals} \\ $$$$\mathrm{will}\:\:\mathrm{double}\:\:\mathrm{in}\:\:\mathrm{size}\:\:\mathrm{every}\:\:\mathrm{12}\:\:\mathrm{years}. \\ $$$$\mathrm{The}\:\:\mathrm{population}\:\:\mathrm{at}\:\:\mathrm{the}\:\:\mathrm{beginning}\:\:\mathrm{of}\:\:\mathrm{2014} \\ $$$$\mathrm{was}\:\:\mathrm{estimated}\:\:\mathrm{to}\:\mathrm{be}\:\:\mathrm{50}\:\:\mathrm{animals}. \\ $$$$\mathrm{If}\:\:{P}\:\:\mathrm{represents}\:\:\mathrm{the}\:\:\mathrm{population}\:\:{n}\:\:\mathrm{years}\:\:\mathrm{after}\:\:\mathrm{2014}. \\ $$$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{equations}\:\:\mathrm{represents}\:\:\mathrm{the}\:\:\mathrm{class}\:\:\mathrm{model} \\ $$$$\mathrm{of}\:\:\mathrm{the}\:\:\mathrm{population}\:\:\mathrm{over}\:\:\mathrm{time}? \\ $$

Question Number 175277 Answers: 0 Comments: 0

Question Number 175279 Answers: 3 Comments: 0

Find the angle between the lines r = ((1),(0),(4) ) + λ ((2),((−1)),((−1)) ) r = ((1),(0),(4) ) + λ ((3),(0),(1) )

$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{angle}\:\:\mathrm{between}\:\:\mathrm{the}\:\:\mathrm{lines} \\ $$$${r}\:=\:\begin{pmatrix}{\mathrm{1}}\\{\mathrm{0}}\\{\mathrm{4}}\end{pmatrix}\:\:+\:\lambda\begin{pmatrix}{\mathrm{2}}\\{−\mathrm{1}}\\{−\mathrm{1}}\end{pmatrix} \\ $$$${r}\:=\:\begin{pmatrix}{\mathrm{1}}\\{\mathrm{0}}\\{\mathrm{4}}\end{pmatrix}\:\:+\:\lambda\begin{pmatrix}{\mathrm{3}}\\{\mathrm{0}}\\{\mathrm{1}}\end{pmatrix} \\ $$$$ \\ $$

Question Number 175275 Answers: 1 Comments: 0

Question Number 181521 Answers: 2 Comments: 0

Find the range of x such that { ((sinx>0)),(((√3)sinx+cosx>0)),((0<x<2π)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\begin{cases}{\mathrm{sin}{x}>\mathrm{0}}\\{\sqrt{\mathrm{3}}\mathrm{sin}{x}+\mathrm{cos}{x}>\mathrm{0}}\\{\mathrm{0}<{x}<\mathrm{2}\pi}\end{cases} \\ $$

Question Number 175266 Answers: 0 Comments: 1

Find matrix ∣A∣A^(-1) given that matrix A= (((√2),(-1),1,( 0)),(4,3,2,(-1)),(0,2,3,( 1)),(1,(-1),0,( 1)) ) using row operations

$$\mathrm{Find}\:\mathrm{matrix}\:\mid\mathrm{A}\mid\mathrm{A}^{-\mathrm{1}} \: \\ $$$$\mathrm{given}\:\mathrm{that}\:\mathrm{matrix}\: \\ $$$$\mathrm{A}=\begin{pmatrix}{\sqrt{\mathrm{2}}}&{-\mathrm{1}}&{\mathrm{1}}&{\:\mathrm{0}}\\{\mathrm{4}}&{\mathrm{3}}&{\mathrm{2}}&{-\mathrm{1}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{3}}&{\:\mathrm{1}}\\{\mathrm{1}}&{-\mathrm{1}}&{\mathrm{0}}&{\:\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{using}\:\mathrm{row}\:\mathrm{operations} \\ $$

Question Number 175265 Answers: 1 Comments: 0

Given that matrix B= { (( (√3))),((-(√5))) :} {: (( (√2))),(( (√7))) } find B^(-1) using row operation

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{matrix}\: \\ $$$$\mathrm{B}=\begin{cases}{\:\:\sqrt{\mathrm{3}}}\\{-\sqrt{\mathrm{5}}}\end{cases}\left.\begin{matrix}{\:\:\:\:\sqrt{\mathrm{2}}}\\{\:\:\:\:\sqrt{\mathrm{7}}}\end{matrix}\right\}\:\mathrm{find}\: \\ $$$$\mathrm{B}^{-\mathrm{1}} \:\mathrm{using}\:\mathrm{row}\:\mathrm{operation} \\ $$

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Question Number 175251 Answers: 1 Comments: 0

Given that 4(x−3)^2 +9(y+2)^2 =27 graph the ellipse

$$\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\mathrm{4}\left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{9}\left(\boldsymbol{\mathrm{y}}+\mathrm{2}\right)^{\mathrm{2}} =\mathrm{27} \\ $$$$\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ellipse}} \\ $$

Question Number 175250 Answers: 0 Comments: 0

If in △ABC and A = ((2π)/3) then: ((√(1/(sinB))))^3 + ((√(1/(sinC))))^3 ≥ 4 (√2)

$$\mathrm{If}\:\mathrm{in}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{and}\:\:\mathrm{A}\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:\mathrm{then}: \\ $$$$\left(\sqrt{\frac{\mathrm{1}}{\mathrm{sinB}}}\right)^{\mathrm{3}} +\:\left(\sqrt{\frac{\mathrm{1}}{\mathrm{sinC}}}\right)^{\mathrm{3}} \geqslant\:\mathrm{4}\:\sqrt{\mathrm{2}} \\ $$

Question Number 175247 Answers: 2 Comments: 0

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prove that ∫_0 ^a ∫_0 ^(√(a^2 −x^2 )) ((dx dy)/((1+e^y )(√(a^2 −x^2 −y^2 )))) = (π/2)log ((2e^a )/(1+e^a ))

$$\:{prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \int_{\mathrm{0}} ^{\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \frac{{dx}\:{dy}}{\left(\mathrm{1}+{e}^{{y}} \right)\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}\:=\:\frac{\pi}{\mathrm{2}}\mathrm{log}\:\frac{\mathrm{2}{e}^{{a}} }{\mathrm{1}+{e}^{{a}} } \\ $$

Question Number 175237 Answers: 0 Comments: 0

The equations of the sides AC, BC and AB of a right−angled triangled with lengths a, b and c are y = −7, x=11 and 4x−3y−5=0 respectively. Find the equation of the inscribed circle of the triangle, if its radius r, is given by r = ((a+b−c)/2).

$$\mathrm{The}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\:\mathrm{AC},\:\mathrm{BC} \\ $$$$\mathrm{and}\:\mathrm{AB}\:\mathrm{of}\:\:\mathrm{a}\:\mathrm{right}−\mathrm{angled}\:\mathrm{triangled} \\ $$$$\mathrm{with}\:\mathrm{lengths}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:{y}\:=\:−\mathrm{7}, \\ $$$${x}=\mathrm{11}\:\mathrm{and}\:\mathrm{4}{x}−\mathrm{3}{y}−\mathrm{5}=\mathrm{0}\:\mathrm{respectively}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{inscribed} \\ $$$$\mathrm{circle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{if}\:\mathrm{its}\:\mathrm{radius}\:{r}, \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{r}\:=\:\frac{{a}+{b}−{c}}{\mathrm{2}}. \\ $$

Question Number 181485 Answers: 2 Comments: 0

two medians of a triange are 3 and 4 cm respectively. find the maximum area of the triangle.

$${two}\:{medians}\:{of}\:{a}\:{triange}\:{are}\:\mathrm{3}\:{and} \\ $$$$\mathrm{4}\:{cm}\:{respectively}.\:{find}\:{the}\:{maximum} \\ $$$${area}\:{of}\:{the}\:{triangle}. \\ $$

Question Number 181484 Answers: 0 Comments: 6

If a hen and a half lay an egg and a half in a day and a half how many eggs would one hen lay in one day?

$${If}\:{a}\:{hen}\:{and}\:{a}\:{half} \\ $$$${lay}\:{an}\:{egg}\:{and}\:{a}\:{half} \\ $$$${in}\:{a}\:{day}\:{and}\:{a}\:{half} \\ $$$${how}\:{many}\:{eggs}\:{would} \\ $$$${one}\:{hen}\:{lay}\:{in}\:{one} \\ $$$${day}? \\ $$

Question Number 175240 Answers: 1 Comments: 1

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