Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 331

Question Number 187400    Answers: 1   Comments: 0

a,b∈C determinant (((a+b a 0 … 0)),(( b a+b ⋱ ⋱ ⋮)),(( 0 ⋱ ⋱ ⋱ 0)),(( ⋮ ⋱ ⋱ ⋱ a)),(( 0 … 0 b a+b)))=?

$$\mathrm{a},\mathrm{b}\in\mathbb{C} \\ $$$$\:\begin{vmatrix}{\mathrm{a}+\mathrm{b}\:\:\:\:\:\:\:\:\:\mathrm{a}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\ldots\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\:\:\:\mathrm{b}\:\:\:\:\:\:\:\:\:\:\mathrm{a}+\mathrm{b}\:\:\:\:\:\:\ddots\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\:\:\:\:\:\vdots}\\{\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\:\:\vdots\:\:\:\:\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\:\:\ddots\:\:\:\:\:\:\ddots\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}}\\{\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\ldots\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{b}\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}+\mathrm{b}}\end{vmatrix}=? \\ $$

Question Number 187394    Answers: 1   Comments: 1

Question Number 187390    Answers: 2   Comments: 0

odd number (2n+1) The sum of twelve consecutive natural numbers is 288. Find the largest natural number

$${odd}\:{number}\:\left(\mathrm{2}{n}+\mathrm{1}\right) \\ $$The sum of twelve consecutive natural numbers is 288. Find the largest natural number

Question Number 187388    Answers: 2   Comments: 0

p^3 +q^3 =c , pq=(1/3) ∀ 0<c<(2/(3(√3))) Find p+q.

$${p}^{\mathrm{3}} +{q}^{\mathrm{3}} ={c}\:\:\:,\:\:{pq}=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\forall\:\:\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$${Find}\:{p}+{q}. \\ $$

Question Number 187381    Answers: 2   Comments: 0

3^x =5^y =225 Determiner: (1/x)+(1/y) ?

$$\mathrm{3}^{{x}} =\mathrm{5}^{{y}} =\mathrm{225} \\ $$$${Determiner}:\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:? \\ $$

Question Number 187379    Answers: 2   Comments: 0

if x and y are +ve integers x+xy+y=54 x+y=?

$${if}\:{x}\:{and}\:{y}\:{are}\:+{ve}\:{integers} \\ $$$${x}+{xy}+{y}=\mathrm{54} \\ $$$${x}+{y}=? \\ $$

Question Number 187377    Answers: 1   Comments: 1

Question Number 187376    Answers: 1   Comments: 0

Question Number 187375    Answers: 0   Comments: 2

Question Number 187374    Answers: 0   Comments: 2

∫(√((t+1)/(t(k−t))))dt=?

$$\int\sqrt{\frac{{t}+\mathrm{1}}{{t}\left({k}−{t}\right)}}{dt}=? \\ $$

Question Number 187373    Answers: 0   Comments: 0

Solve for natural numbers: 31 + Σ_(k=1) ^n ( ((n),(k) ) ∙ Σ_(m=1) ^n m^(n−k) ) = 31^(30)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$

Question Number 187364    Answers: 2   Comments: 3

Question Number 187362    Answers: 2   Comments: 1

Question Number 187359    Answers: 1   Comments: 0

what are the two complex solution to X^(−x) +(−X)^x =0 in addition to ±1 ?

$$ \\ $$$${what}\:{are}\:{the}\:{two}\:{complex}\:{solution}\:{to} \\ $$$${X}^{−{x}} +\left(−{X}\right)^{{x}} =\mathrm{0}\:{in}\:{addition}\:{to}\:\pm\mathrm{1}\:? \\ $$

Question Number 187357    Answers: 1   Comments: 0

Question Number 187355    Answers: 1   Comments: 2

Question Number 187340    Answers: 0   Comments: 0

Question Number 187336    Answers: 1   Comments: 0

solve for x if X^x •5^x −5^(2+x) =0

$${solve}\:{for}\:{x}\:{if} \\ $$$${X}^{{x}} \bullet\mathrm{5}^{{x}} −\mathrm{5}^{\mathrm{2}+{x}} =\mathrm{0} \\ $$$$ \\ $$

Question Number 187335    Answers: 1   Comments: 0

Apply the rotation of coordinates given by the following matrix to the equation xy=1; what is the equation in th uv coordinate system? [(u),(v) ]= [((cos45 sin45)),((−sin45 cos45)) ] [(x),(y) ]

$${Apply}\:{the}\:{rotation}\:{of}\:{coordinates}\:{given} \\ $$$${by}\:{the}\:{following}\:{matrix}\:{to}\:{the}\:{equation}\: \\ $$$${xy}=\mathrm{1};\:{what}\:{is}\:{the}\:{equation}\:{in}\:{th}\:{uv}\:{coordinate}\: \\ $$$${system}? \\ $$$$\begin{bmatrix}{{u}}\\{{v}}\end{bmatrix}=\begin{bmatrix}{{cos}\mathrm{45}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{sin}\mathrm{45}}\\{−{sin}\mathrm{45}\:\:\:\:\:\:\:\:\:\:{cos}\mathrm{45}}\end{bmatrix}\begin{bmatrix}{{x}}\\{{y}}\end{bmatrix} \\ $$

Question Number 187330    Answers: 1   Comments: 0

show that ((1−cosθ)/(1+cosθ))=tan^2 ((1/2)θ)

$$ \\ $$$${show}\:{that}\:\frac{\mathrm{1}−{cos}\theta}{\mathrm{1}+{cos}\theta}={tan}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)\:\:\: \\ $$

Question Number 187324    Answers: 1   Comments: 0

calculate the unit of the chord which is 6cm from the center of the circle of radius 10cm

$${calculate}\:\:{the}\:{unit}\:{of}\:{the}\:\:{chord}\:{which}\:{is} \\ $$$$\mathrm{6}{cm}\:{from}\:{the}\:{center}\:{of}\:\:{the}\:\:{circle}\:{of}\:{radius}\:\mathrm{10}{cm} \\ $$$$ \\ $$$$ \\ $$

Question Number 187317    Answers: 2   Comments: 0

∫(dx/(x(√(1−2x))))

$$\int\frac{{dx}}{{x}\sqrt{\mathrm{1}−\mathrm{2}{x}}} \\ $$

Question Number 187312    Answers: 0   Comments: 1

Question Number 187311    Answers: 0   Comments: 2

If f_k (x)=(1/k)(sin^k x+cos^k x) find f_4 (x)−f_6 (x) f_4 (x)−f_6 (x)=(1/4)(sin^4 x +cos^4 x)−(1/6)(sin^6 x+cos^6 x) =(1/2)sin^4 x((1/2)−(1/3)sin^2 x)+(1/2)cos^4 x((1/2)−(1/3)cos^2 x)

$$\mathrm{If}\:{f}_{{k}} \left({x}\right)=\frac{\mathrm{1}}{{k}}\left(\mathrm{sin}\:^{{k}} {x}+\mathrm{cos}\:^{{k}} {x}\right)\:\mathrm{find}\:{f}_{\mathrm{4}} \left({x}\right)−{f}_{\mathrm{6}} \left({x}\right) \\ $$$${f}_{\mathrm{4}} \left({x}\right)−{f}_{\mathrm{6}} \left({x}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{sin}\:^{\mathrm{4}} {x}\:+\mathrm{cos}\:^{\mathrm{4}} {x}\right)−\frac{\mathrm{1}}{\mathrm{6}}\left(\mathrm{sin}\:^{\mathrm{6}} {x}+\mathrm{cos}\:^{\mathrm{6}} {x}\right) \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{4}} {x}\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{sin}\:^{\mathrm{2}} {x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:^{\mathrm{4}} {x}\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{cos}\:^{\mathrm{2}} {x}\right) \\ $$

Question Number 187302    Answers: 0   Comments: 0

f(4)=44, f(m)=52,f(l)=−33 l,m are positive integers such that 4<m<l and f(x) is a polynomial with integer coefficients. Find l+m.

$${f}\left(\mathrm{4}\right)=\mathrm{44},\:{f}\left({m}\right)=\mathrm{52},{f}\left({l}\right)=−\mathrm{33} \\ $$$${l},{m}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}<{m}<{l} \\ $$$$\mathrm{and}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}. \\ $$$$\mathrm{Find}\:{l}+{m}. \\ $$

Question Number 187301    Answers: 2   Comments: 0

  Pg 326      Pg 327      Pg 328      Pg 329      Pg 330      Pg 331      Pg 332      Pg 333      Pg 334      Pg 335   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com