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Question Number 175953    Answers: 1   Comments: 0

Question Number 175925    Answers: 1   Comments: 1

1^x +6^x +8^x =9^x find x ? Mastermind

$$\mathrm{1}^{\mathrm{x}} +\mathrm{6}^{\mathrm{x}} +\mathrm{8}^{\mathrm{x}} =\mathrm{9}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 175888    Answers: 1   Comments: 0

Solve the differential equation (dy/dx)=((1+y^2 )/(y(1−x^2 )))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }{\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)} \\ $$

Question Number 175746    Answers: 1   Comments: 0

Solve the differential equation 2(2xy+4y−3)dx+(x+2)^2 dy=0 Mastermind

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{2}\left(\mathrm{2xy}+\mathrm{4y}−\mathrm{3}\right)\mathrm{dx}+\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \mathrm{dy}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 181509    Answers: 1   Comments: 0

Solve: (dy/dx)=((y^2 −3xy−5x^2 )/x^2 ) y(1)=−1 M.m

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}^{\mathrm{2}} −\mathrm{3xy}−\mathrm{5x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{1}\right)=−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 175655    Answers: 1   Comments: 0

Question Number 175624    Answers: 3   Comments: 0

let p(x) = x^6 +ax^5 +bx^4 +cx^3 +dx^2 +ex+f be a polynomial function such that p(1) = 1 ; p(2) = 2 ; p(3) = 3 p(4) = 4 ; p(5) = 5 ; p(6) = 6 then find p(7) = ?

$$\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{6}} +\mathrm{ax}^{\mathrm{5}} +\mathrm{bx}^{\mathrm{4}} +\mathrm{cx}^{\mathrm{3}} +\mathrm{dx}^{\mathrm{2}} +\mathrm{ex}+\mathrm{f} \\ $$$$\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function}\:\mathrm{such} \\ $$$$\:\:\mathrm{that}\:\:\mathrm{p}\left(\mathrm{1}\right)\:=\:\mathrm{1}\:;\:\mathrm{p}\left(\mathrm{2}\right)\:=\:\mathrm{2}\:;\:\:\mathrm{p}\left(\mathrm{3}\right)\:=\:\mathrm{3} \\ $$$$\:\:\mathrm{p}\left(\mathrm{4}\right)\:=\:\mathrm{4}\:;\:\mathrm{p}\left(\mathrm{5}\right)\:=\:\mathrm{5}\:;\:\mathrm{p}\left(\mathrm{6}\right)\:=\:\mathrm{6}\:\:\mathrm{then} \\ $$$$\:\:\mathrm{find}\:\:\mathrm{p}\left(\mathrm{7}\right)\:=\:? \\ $$

Question Number 175426    Answers: 0   Comments: 0

Question Number 175369    Answers: 1   Comments: 0

solve for x log_(∣sinx∣ ) (x^2 −8x+23) > (3/(log_2 ∣sinx∣ ))

$$\:\:\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\:\:\:\mathrm{log}_{\mid\mathrm{sin}{x}\mid\:} \left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{23}\right)\:>\:\frac{\mathrm{3}}{\mathrm{log}_{\mathrm{2}} \mid\mathrm{sin}{x}\mid\:} \\ $$

Question Number 175335    Answers: 2   Comments: 0

solve the inequalities Q.(1) ((1+log_a ^2 x)/(1+log_a x)) > 1 , 0<a<1 Q.(2) log_x ((4x+5)/(6−5x)) < −1

$$\:\:\:\:\:\mathrm{solve}\:\mathrm{the}\:\mathrm{inequalities} \\ $$$$\:{Q}.\left(\mathrm{1}\right)\:\:\frac{\mathrm{1}+\mathrm{log}_{{a}} ^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{log}_{{a}} {x}}\:\:\:>\:\mathrm{1}\:\:\:,\:\:\mathrm{0}<{a}<\mathrm{1} \\ $$$$\:\:{Q}.\left(\mathrm{2}\right)\:\:\:\:\:\:\:\mathrm{log}_{{x}} \:\frac{\mathrm{4}{x}+\mathrm{5}}{\mathrm{6}−\mathrm{5}{x}}\:\:<\:\:−\mathrm{1} \\ $$

Question Number 175213    Answers: 2   Comments: 0

Solve by Method of variation parameter (d^2 y/dx^2 )−3(dy/dx)+2y=sinx M.m

$$\mathrm{Solve}\:\mathrm{by}\:\mathrm{Method}\:\mathrm{of}\:\mathrm{variation}\:\mathrm{parameter} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }−\mathrm{3}\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{2y}=\mathrm{sinx} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 175122    Answers: 1   Comments: 0

Question Number 175108    Answers: 1   Comments: 0

Question Number 175010    Answers: 1   Comments: 1

A ball of p of mass 0.25kg losses (1/3) of its velocity when it makes an head on collision with an identical ball q at rest. After collision, q moves off with a velocity of 2ms^(−1) in the original direction of p. Calculate the initial velocity of p.

$$\:\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{losses}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of}\: \\ $$$$\mathrm{its}\:\mathrm{velocity}\:\mathrm{when}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{head}\:\mathrm{on} \\ $$$$\mathrm{collision}\:\mathrm{with}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{ball}\:\boldsymbol{\mathrm{q}}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{After}\:\mathrm{collision},\:\boldsymbol{\mathrm{q}}\:\mathrm{moves}\:\mathrm{off}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{2ms}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$

Question Number 174950    Answers: 1   Comments: 0

Have you seen this method of solving quadratic problem? x^2 −x−12=0 y′=±(√(b^2 −4ac))

$$\mathrm{Have}\:\mathrm{you}\:\mathrm{seen}\:\mathrm{this}\:\mathrm{method}\:\mathrm{of}\:\mathrm{solving} \\ $$$$\mathrm{quadratic}\:\mathrm{problem}? \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{12}=\mathrm{0} \\ $$$$\mathrm{y}'=\pm\sqrt{\mathrm{b}^{\mathrm{2}} −\mathrm{4ac}} \\ $$

Question Number 174928    Answers: 3   Comments: 0

How many digits does 1000^(1000) have? Mastermind

$$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{does}\:\mathrm{1000}^{\mathrm{1000}} \:\mathrm{have}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174853    Answers: 0   Comments: 2

By first principle, solve cos^2 x + sin^2 x=1

$$\mathrm{By}\:\mathrm{first}\:\mathrm{principle},\:\mathrm{solve}\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}=\mathrm{1} \\ $$

Question Number 174770    Answers: 1   Comments: 0

∫(((sinx)/( (√x))))dx Mastermind

$$\int\left(\frac{\mathrm{sinx}}{\:\sqrt{\mathrm{x}}}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174742    Answers: 0   Comments: 0

≪_• ^• I THINK...^ ^(−) _•^• _(−) ≫ One question per post, IDEAL 👍👍👍 Two questions per post,OK (BEARABLE) (👎+👍)/2 Three or more questions:NO, NO, NO! 👎👎👎

$$\:\:\:\:\:\ll_{\bullet} ^{\bullet} \underset{−} {\overline {\boldsymbol{\mathrm{I}}\:\boldsymbol{\mathrm{THINK}}...^{} }}\:_{\bullet} ^{\bullet} \gg \\ $$$$\boldsymbol{\mathrm{One}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{per}}\:\boldsymbol{\mathrm{post}},\:\boldsymbol{\mathrm{IDEAL}} \\ $$👍👍👍 $$\boldsymbol{\mathrm{Two}}\:\boldsymbol{\mathrm{questions}}\:\boldsymbol{\mathrm{per}}\:\boldsymbol{\mathrm{post}},\boldsymbol{\mathrm{OK}}\:\left(\boldsymbol{\mathrm{BEARABLE}}\right) \\ $$(👎+👍)/2 $$\boldsymbol{\mathrm{Three}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{more}}\:\boldsymbol{\mathrm{questions}}:\boldsymbol{\mathrm{NO}},\:\boldsymbol{\mathrm{NO}},\:\boldsymbol{\mathrm{NO}}! \\ $$👎👎👎

Question Number 174661    Answers: 1   Comments: 0

After being marked down 20 percent. a calculator sells for $10. The Original selling price was ?

$$\mathrm{After}\:\mathrm{being}\:\mathrm{marked}\:\mathrm{down}\:\mathrm{20}\:\mathrm{percent}. \\ $$$$\mathrm{a}\:\mathrm{calculator}\:\mathrm{sells}\:\mathrm{for}\:\$\mathrm{10}.\:\mathrm{The}\:\mathrm{Original} \\ $$$$\mathrm{selling}\:\mathrm{price}\:\mathrm{was}\:? \\ $$

Question Number 174619    Answers: 2   Comments: 0

Question Number 174613    Answers: 1   Comments: 0

In a mixture of Skettles and M&M′s, 80% of the pieces are M&M′s. A fourth of this mixture is replaced by a second mixture, resulting in combination which contain 16% Skittles in total. What was the percentage of Skittles in the second mixture?

$$\mathrm{In}\:\mathrm{a}\:\mathrm{mixture}\:\mathrm{of}\:\:\mathrm{Skettles}\:\mathrm{and}\:\mathrm{M\&M}'\mathrm{s}, \\ $$$$\mathrm{80\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pieces}\:\mathrm{are}\:\mathrm{M\&M}'\mathrm{s}.\:\mathrm{A}\:\mathrm{fourth} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{by}\:\mathrm{a}\:\mathrm{second} \\ $$$$\mathrm{mixture},\:\mathrm{resulting}\:\mathrm{in}\:\mathrm{combination} \\ $$$$\mathrm{which}\:\mathrm{contain}\:\mathrm{16\%}\:\mathrm{Skittles}\:\mathrm{in}\:\mathrm{total}. \\ $$$$\mathrm{What}\:\mathrm{was}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{Skittles} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{mixture}? \\ $$

Question Number 174612    Answers: 0   Comments: 1

Question Number 174594    Answers: 1   Comments: 0

Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number. show that σ(n)<2n holds true for all n of the form n=p^2 . Mastermind

$$\mathrm{Let}\:\sigma\left(\mathrm{n}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive} \\ $$$$\mathrm{divisors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{and}\:\mathrm{let}\:\mathrm{p}\:\mathrm{be} \\ $$$$\mathrm{any}\:\mathrm{prime}\:\mathrm{number}.\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\sigma\left(\mathrm{n}\right)<\mathrm{2n}\:\mathrm{holds}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{form}\:\mathrm{n}=\mathrm{p}^{\mathrm{2}} . \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174591    Answers: 1   Comments: 0

The drawing below shows two equilateral triangles with side length a. The triangle are horizontally shifted by (a/2). Find the intersection area A of the two triangles (grey area).

$$\mathrm{The}\:\mathrm{drawing}\:\mathrm{below}\:\mathrm{shows}\:\mathrm{two}\: \\ $$$$\mathrm{equilateral}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length} \\ $$$$\boldsymbol{\mathrm{a}}.\:\mathrm{The}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{horizontally}\:\mathrm{shifted} \\ $$$$\mathrm{by}\:\frac{\mathrm{a}}{\mathrm{2}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{area}\:\mathrm{A}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{triangles}\:\left(\mathrm{grey}\:\mathrm{area}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 174528    Answers: 1   Comments: 0

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