Question and Answers Forum

AllQuestion and Answers: Page 1678

Question Number 39607 Answers: 3 Comments: 0

find the minimum and maximum value of the quadratic functions a) 4x^2 + 5x + 1 b) x + (2/x) = 3 c) x^2 − (x/4) + 6 hence draw each draw

$${find}\:{the}\: \\ $$$${minimum}\:{and}\:{maximum}\:{value} \\ $$$${of}\:{the}\:{quadratic}\:{functions} \\ $$$$\left.{a}\right)\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{1} \\ $$$$\left.{b}\right)\:{x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{3} \\ $$$$\left.{c}\right)\:{x}^{\mathrm{2}} \:−\:\frac{{x}}{\mathrm{4}}\:+\:\mathrm{6} \\ $$$${hence}\:{draw}\:{each}\:{draw} \\ $$

Question Number 39591 Answers: 1 Comments: 0

Given the lines l_1 :−3mx + 3y = 9 and l_(2 ) : y = mx + c find the value of m and c if the point (1,2) lie on both lines. hence the tangent of the curve y = (mx + c)^2 when it moves across the x−axis

$${Given}\:{the}\:{lines}\: \\ $$$${l}_{\mathrm{1}} :−\mathrm{3}{mx}\:+\:\mathrm{3}{y}\:=\:\mathrm{9}\: \\ $$$${and}\:{l}_{\mathrm{2}\:} :\:{y}\:=\:{mx}\:+\:{c} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}\:{and}\:{c}\:{if} \\ $$$${the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right)\:{lie}\:{on}\:{both}\:{lines}. \\ $$$${hence}\:{the}\:{tangent}\:{of}\:{the} \\ $$$${curve}\:{y}\:=\:\left({mx}\:+\:{c}\right)^{\mathrm{2}} \\ $$$${when}\:{it}\:{moves}\:{across}\:{the}\:{x}−{axis} \\ $$

Question Number 39588 Answers: 1 Comments: 0

if cos A= (3/5) and tan B = ((12)/5) where A and B are reflex angles find without using tables,the value of a) sin (A − B) b) tan(A−B) c) cos (A + B).

$${if}\:{cos}\:{A}=\:\frac{\mathrm{3}}{\mathrm{5}}\:{and}\:{tan}\:{B}\:=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$${where}\:{A}\:{and}\:{B}\:{are}\:{reflex}\:{angles} \\ $$$${find}\:{without}\:{using}\:{tables},{the} \\ $$$${value}\:{of} \\ $$$$\left.{a}\left.\right)\:{sin}\:\left({A}\:−\:{B}\right)\:{b}\right)\:{tan}\left({A}−{B}\right) \\ $$$$\left.{c}\right)\:{cos}\:\left({A}\:+\:{B}\right). \\ $$

Question Number 39587 Answers: 4 Comments: 0

Solve for x in the range 0 ≤ x ≤2π the equations a) cos(x + (π/3)) = 0 b) sin x = cos x. c) sin 2x + 2sin x = 1 + cos x

$${Solve}\:{for}\:{x}\:{in}\:{the}\:{range}\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\mathrm{2}\pi \\ $$$${the}\:{equations} \\ $$$$\left.{a}\right)\:{cos}\left({x}\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\mathrm{0}\: \\ $$$$\left.{b}\right)\:{sin}\:{x}\:=\:{cos}\:{x}. \\ $$$$\left.{c}\right)\:{sin}\:\mathrm{2}{x}\:+\:\mathrm{2}{sin}\:{x}\:=\:\mathrm{1}\:+\:{cos}\:{x} \\ $$$$ \\ $$

Question Number 39586 Answers: 2 Comments: 0

show that a) ((1 + 2sin2θ − cos2θ)/(1+sin2θ + cos 2θ)) = tan θ b) tan^2 A − tan^2 B = ((sin^2 A−sin^2 B)/(cos^2 A cos^2 B))

$${show}\:{that}\: \\ $$$$\left.{a}\right)\:\frac{\mathrm{1}\:+\:\mathrm{2}{sin}\mathrm{2}\theta\:−\:{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta\:+\:{cos}\:\mathrm{2}\theta}\:=\:{tan}\:\theta \\ $$$$\left.{b}\right)\:{tan}^{\mathrm{2}} {A}\:−\:{tan}^{\mathrm{2}} {B}\:=\:\frac{{sin}^{\mathrm{2}} {A}−{sin}^{\mathrm{2}} {B}}{{cos}^{\mathrm{2}} {A}\:{cos}^{\mathrm{2}} {B}} \\ $$$$ \\ $$$$ \\ $$

Question Number 39582 Answers: 1 Comments: 0

Question Number 39573 Answers: 1 Comments: 1

Point charges 88μC,−55μC and 70μC are placed in a straight line. The central one is 0.75m from each of the others.Calculate the net force on each due to the other two.

$${Point}\:{charges}\:\mathrm{88}\mu{C},−\mathrm{55}\mu{C}\:{and} \\ $$$$\mathrm{70}\mu{C}\:{are}\:{placed}\:{in}\:{a}\:{straight}\:{line}. \\ $$$${The}\:{central}\:{one}\:{is}\:\mathrm{0}.\mathrm{75}{m}\:{from} \\ $$$${each}\:{of}\:{the}\:{others}.{Calculate}\:{the} \\ $$$${net}\:{force}\:{on}\:{each}\:{due}\:{to}\:{the}\:{other} \\ $$$${two}. \\ $$

Question Number 39559 Answers: 2 Comments: 1

Question Number 39529 Answers: 0 Comments: 5

Question Number 39520 Answers: 1 Comments: 1

if (1+x)^n =Σ_(i=0) ^n a_i x^i and (1+x)^(n+1) =Σ_(i=0) ^(n+1) b_i x^i calculate ((∐_(i=0) ^n a_i )/(Π_(i=0) ^(n+1) b_i )) .

$${if}\:\left(\mathrm{1}+{x}\right)^{{n}} \:=\sum_{{i}=\mathrm{0}} ^{{n}} \:{a}_{{i}} {x}^{{i}} \:\:\:\:{and} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}+\mathrm{1}} \:=\sum_{{i}=\mathrm{0}} ^{{n}+\mathrm{1}} \:{b}_{{i}} \:{x}^{{i}} \:\:{calculate} \\ $$$$\frac{\coprod_{{i}=\mathrm{0}} ^{{n}} \:{a}_{{i}} }{\prod_{{i}=\mathrm{0}} ^{{n}+\mathrm{1}} \:{b}_{{i}} }\:. \\ $$

Question Number 39519 Answers: 1 Comments: 1

simplify 1) A_n =(1/(√a)){ (((1+(√a))/2) )^n −(((1−(√a))/2))^n } with n natural integr and a>0 2) f(x)= (1/(√(2x+1))){ (((1+(√(2x+1)))/2))^n −(((1−(√(2x+1)))/2))^n }

$${simplify}\: \\ $$$$\left.\mathrm{1}\right)\:{A}_{{n}} =\frac{\mathrm{1}}{\sqrt{{a}}}\left\{\:\left(\frac{\mathrm{1}+\sqrt{{a}}}{\mathrm{2}}\:\right)^{{n}} \:−\left(\frac{\mathrm{1}−\sqrt{{a}}}{\mathrm{2}}\right)^{{n}} \right\}\:{with}\:{n}\:{natural}\: \\ $$$${integr}\:{and}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}{x}+\mathrm{1}}}\left\{\:\left(\frac{\mathrm{1}+\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} \:−\left(\frac{\mathrm{1}−\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} \right\} \\ $$

Question Number 39517 Answers: 0 Comments: 2

find radius of S(x)=Σ_(n=1) ^∞ (x^n /n^2 ) and calculate its sum 2) find Σ_(n=1) ^∞ (1/n^2 ) and Σ_(n=1) ^∞ (1/(n^2 2^n )) .

$${find}\:{radius}\:{of}\:\:{S}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${and}\:{calculate}\:{its}\:{sum} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:\:{and}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:\mathrm{2}^{{n}} }\:. \\ $$$$ \\ $$

Question Number 39524 Answers: 0 Comments: 0

Question Number 39511 Answers: 0 Comments: 2

Question Number 39508 Answers: 1 Comments: 1

Question Number 39486 Answers: 0 Comments: 7

sin θ=sin αsin (((θ+α)/2)) Express θ explicitly in terms of α.

$$\mathrm{sin}\:\theta=\mathrm{sin}\:\alpha\mathrm{sin}\:\left(\frac{\theta+\alpha}{\mathrm{2}}\right) \\ $$$${Express}\:\theta\:{explicitly}\:{in}\:{terms}\:{of}\:\alpha. \\ $$

Question Number 39475 Answers: 1 Comments: 0

Question Number 39470 Answers: 2 Comments: 2

Question Number 39469 Answers: 1 Comments: 0

Question Number 39466 Answers: 0 Comments: 1

Question Number 39464 Answers: 1 Comments: 0

Domain of the explicit form of the function y represented implicitly by the equation (1+x)cosy−x^2 =0 is (a) (−1,1] (b) (−1, 1−(√)5/2] (c) [1−(√)5/2, 1+(√)5/2] (d) [0, 1+(√)5/2]

$${Domain}\:\:{of}\:\:{the}\:\:{explicit}\:\:{form}\:\:{of} \\ $$$${the}\:\:{function}\:\:\:{y}\:\:\:{represented}\: \\ $$$${implicitly}\:\:\:{by}\:\:{the}\:\:{equation}\: \\ $$$$\left(\mathrm{1}+{x}\right){cosy}−{x}^{\mathrm{2}} =\mathrm{0}\:\:{is} \\ $$$$\left({a}\right)\:\:\left(−\mathrm{1},\mathrm{1}\right]\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\:\:\:\left(−\mathrm{1},\:\mathrm{1}−\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$$$\left({c}\right)\:\:\:\left[\mathrm{1}−\sqrt{}\mathrm{5}/\mathrm{2},\:\mathrm{1}+\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$$$\left({d}\right)\:\:\left[\mathrm{0},\:\mathrm{1}+\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$

Question Number 39458 Answers: 0 Comments: 4

find the greatest possible square insribed in a triangle with sides a b c

$$\mathrm{find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{possible}\:\mathrm{square}\:\mathrm{insribed}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{sides}\:{a}\:{b}\:{c} \\ $$

Question Number 39457 Answers: 1 Comments: 0

Question Number 39443 Answers: 1 Comments: 3

lim_(n→∞) [ (1/(n^2 +1))+ (2/(n^2 +2))+ (3/(n^2 +3))+ ....+(1/(n+1))] = ?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}}+\:\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} +\mathrm{3}}+\:....+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right]\:=\:? \\ $$

Question Number 39441 Answers: 0 Comments: 2

∫_(1/4) ^( 4) (1/x) sin (x−(1/x))dx = ?

$$\int_{\frac{\mathrm{1}}{\mathrm{4}}} ^{\:\mathrm{4}} \:\frac{\mathrm{1}}{{x}}\:\mathrm{sin}\:\left({x}−\frac{\mathrm{1}}{{x}}\right){dx}\:=\:? \\ $$

Question Number 39440 Answers: 1 Comments: 0

f(x)= ∫_0 ^( x_ ) e^(t ) (((1+sin t)/(1+cos t))) dt. Then f((π/3))×f(((2π)/3)) = ?

$$\mathrm{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\:{x}_{} } \:{e}^{{t}\:} \left(\frac{\mathrm{1}+\mathrm{sin}\:{t}}{\mathrm{1}+\mathrm{cos}\:{t}}\right)\:{dt}. \\ $$$${T}\mathrm{hen}\:\:\mathrm{f}\left(\frac{\pi}{\mathrm{3}}\right)×\mathrm{f}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\:=\:? \\ $$

Pg 1673 Pg 1674 Pg 1675 Pg 1676 Pg 1677 Pg 1678 Pg 1679 Pg 1680 Pg 1681 Pg 1682

Contact: info@tinkutara.com