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Question Number 187440 Answers: 0 Comments: 1

if y^(x−y) =(x^2 /y) then x−y=?

$${if}\:\:{y}^{{x}−{y}} =\frac{{x}^{\mathrm{2}} }{{y}}\:{then}\:{x}−{y}=? \\ $$

Question Number 187437 Answers: 1 Comments: 0

Question Number 187433 Answers: 1 Comments: 0

Prove that ▽×▽φ=0. If φ is assumed to be continous and having continous first and second order derivatives. M.m

$$\mathrm{Prove}\:\mathrm{that}\:\bigtriangledown×\bigtriangledown\phi=\mathrm{0}.\:\mathrm{If}\:\phi\:\mathrm{is} \\ $$$$\mathrm{assumed}\:\mathrm{to}\:\mathrm{be}\:\mathrm{continous}\:\mathrm{and} \\ $$$$\mathrm{having}\:\mathrm{continous}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second} \\ $$$$\mathrm{order}\:\mathrm{derivatives}. \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 187408 Answers: 2 Comments: 0

∫((sec^2 x)/( (√(1−tan^2 x))))dx

$$\:\int\frac{\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}{\:\sqrt{\mathrm{1}−\boldsymbol{\mathrm{tan}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 187406 Answers: 1 Comments: 2

3^x .8^(x/(x+2)) =6ln0−log10

$$\mathrm{3}^{{x}} .\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6}{ln}\mathrm{0}−{log}\mathrm{10} \\ $$

Question Number 187401 Answers: 0 Comments: 0

a∈C determinant (((a 1 … 1)),((1 ⋱ ⋱ ⋮)),((⋮ ⋱ ⋱ 1)),((1 … 1 a)))=?

$$\mathrm{a}\in\mathbb{C} \\ $$$$\begin{vmatrix}{\mathrm{a}\:\:\:\mathrm{1}\:\:\:\:\ldots\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\ddots\:\:\ddots\:\:\vdots}\\{\vdots\:\:\ddots\:\:\ddots\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\ldots\:\:\:\:\mathrm{1}\:\:\:\mathrm{a}}\end{vmatrix}=? \\ $$

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)))=?

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)

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

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