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Question Number 46813 Answers: 2 Comments: 1

Question Number 46809 Answers: 1 Comments: 0

an early question for the new year how many rectangular triangles with sides a, b, c ∈N^★ exist with one side =2019

$$\mathrm{an}\:\mathrm{early}\:\mathrm{question}\:\mathrm{for}\:\mathrm{the}\:\mathrm{new}\:\mathrm{year} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{rectangular}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{sides} \\ $$$${a},\:{b},\:{c}\:\in\mathbb{N}^{\bigstar} \:\mathrm{exist}\:\mathrm{with}\:\mathrm{one}\:\mathrm{side}\:=\mathrm{2019} \\ $$

Question Number 46805 Answers: 2 Comments: 0

In an A.p., the sum of first n terms is P , the sum of the next n terms is Q and the sum of further next n terms is R. Show that P, Q, R is an A.P.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{A}.\mathrm{p}.,\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{P}\:,\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{next}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{Q}\:\mathrm{and} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{further}\:\mathrm{next}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{R}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{P},\:\mathrm{Q},\:\mathrm{R}\:\mathrm{is}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$ \\ $$

Question Number 46802 Answers: 0 Comments: 1

Can someone please help me for the following: Solve fot x (exact value with formulas) : 17x^4 + 7x^3 − (√(11))x^2 − 18x + 3 = 0 Thank you

$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{for}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{fot}\:{x}\:\left(\mathrm{exact}\:\mathrm{value}\:\mathrm{with}\:\mathrm{formulas}\right)\:: \\ $$$$ \\ $$$$\mathrm{17}{x}^{\mathrm{4}} \:+\:\mathrm{7}{x}^{\mathrm{3}} \:−\:\sqrt{\mathrm{11}}\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{18}{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 46790 Answers: 0 Comments: 4

Question Number 46760 Answers: 1 Comments: 1

how many natural solutions exist to x+y+z=11, x,y,z∈N

$${how}\:{many}\:{natural}\:{solutions}\:{exist} \\ $$$${to} \\ $$$${x}+{y}+{z}=\mathrm{11},\:{x},{y},{z}\in\mathbb{N} \\ $$

Question Number 46751 Answers: 0 Comments: 3

Prove that there exist 4 distinct positive integers such that each integer divides the sum of the remaining integers.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{4}\:\mathrm{distinct}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{each}\:\mathrm{integer}\:\mathrm{divides}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{remaining}\:\mathrm{integers}.\: \\ $$

Question Number 46748 Answers: 0 Comments: 0

∫(√(sin2x)) dx=??

$$\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$

Question Number 46744 Answers: 1 Comments: 2

calculate S_n =Σ_(0≤i,j≤n) ((i+j)/2^(i+j) )

$${calculate}\:{S}_{{n}} =\sum_{\mathrm{0}\leqslant{i},{j}\leqslant{n}} \:\frac{{i}+{j}}{\mathrm{2}^{{i}+{j}} } \\ $$

Question Number 46740 Answers: 1 Comments: 2

find ∫ x(√((1−(√x))/(1+(√x))))dx

$${find}\:\int\:\:{x}\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}{dx} \\ $$

Question Number 46785 Answers: 1 Comments: 0

Solve the system: x + y + z = 30 ..... equation (i) (x/3) + (y/2) + 2z = 30 ...... equation (ii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{30}\:\:\:\:\:\:\:\:\:.....\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{x}}{\mathrm{3}}\:+\:\frac{\mathrm{y}}{\mathrm{2}}\:+\:\mathrm{2z}\:\:=\:\:\mathrm{30}\:\:\:\:\:......\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 46738 Answers: 0 Comments: 2

please help Write an algorithm that will find the solution of the equation f(x)= { ((−x, when x<0)),((x, when x≥0)) :}

$${please}\:{help} \\ $$$$ \\ $$$${Write}\:{an}\:{algorithm}\:{that}\:{will}\:{find} \\ $$$${the}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\begin{cases}{−{x},\:{when}\:{x}<\mathrm{0}}\\{{x},\:\:\:\:\:{when}\:{x}\geqslant\mathrm{0}}\end{cases} \\ $$

Question Number 46737 Answers: 2 Comments: 0

Question Number 46736 Answers: 2 Comments: 1

Question Number 46735 Answers: 0 Comments: 3

Question Number 46731 Answers: 1 Comments: 1

calculate Σ_((i,j)∈N) ((i^2 +j^2 )/2^(i+j) )

$${calculate}\:\sum_{\left({i},{j}\right)\in{N}} \:\:\frac{{i}^{\mathrm{2}} \:+{j}^{\mathrm{2}} }{\mathrm{2}^{{i}+{j}} } \\ $$

Question Number 46720 Answers: 0 Comments: 6

Question Number 46715 Answers: 0 Comments: 0

Given that the first two terms of a G.P is x and the last two terms is y. Find the common ratio.

$${Given}\:{that}\:{the}\:{first}\:{two}\:{terms}\:{of} \\ $$$${a}\:{G}.{P}\:{is}\:{x}\:{and}\:{the}\:{last}\:{two}\:{terms} \\ $$$${is}\:{y}.\:{Find}\:{the}\:{common}\:{ratio}. \\ $$

Question Number 46713 Answers: 1 Comments: 0

((x−1)/(x−2))−((x−2)/(x−3))=((x−5)/(x−6))−((x−6)/(x−7)) solve for x

$$\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}}−\frac{{x}−\mathrm{2}}{{x}−\mathrm{3}}=\frac{{x}−\mathrm{5}}{{x}−\mathrm{6}}−\frac{{x}−\mathrm{6}}{{x}−\mathrm{7}} \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{for}}\:\boldsymbol{{x}} \\ $$

Question Number 46712 Answers: 0 Comments: 0

find S(z)=Σ_(n=1) ^∞ (z^n /n^2 ) with z complex and ∣z∣=1 .

$${find}\:{S}\left({z}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{z}^{{n}} }{{n}^{\mathrm{2}} }\:{with}\:{z}\:{complex}\:{and}\:\mid{z}\mid=\mathrm{1}\:. \\ $$

Question Number 46708 Answers: 0 Comments: 0

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

Question Number 46705 Answers: 0 Comments: 0

calculate Σ_(k=0) ^n (1/(3k+1)) interms of H_n H_n =Σ_(k=1) ^n (1/k) .

$${calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{interms}\:{of}\:{H}_{{n}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:. \\ $$

Question Number 46697 Answers: 1 Comments: 0

Find the sum of the first nterms of the G.P 3+1+(1/3)+...and show that the sum cannot exceed (9/2) however great n may be.

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{first}\:{nterms}\: \\ $$$${of}\:{the}\:{G}.{P}\:\mathrm{3}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+...{and}\:{show}\:{that} \\ $$$${the}\:{sum}\:{cannot}\:{exceed}\:\frac{\mathrm{9}}{\mathrm{2}}\:{however} \\ $$$${great}\:{n}\:{may}\:{be}. \\ $$

Question Number 46694 Answers: 1 Comments: 0

(y′′y−(y′)^2 )e^((y′)/y) =y^2 not sure if it′s possible to solve this at all...

$$\left({y}''{y}−\left({y}'\right)^{\mathrm{2}} \right)\mathrm{e}^{\frac{{y}'}{{y}}} ={y}^{\mathrm{2}} \\ $$$$\mathrm{not}\:\mathrm{sure}\:\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{at}\:\mathrm{all}... \\ $$

Question Number 46686 Answers: 2 Comments: 1

Question Number 46681 Answers: 1 Comments: 2

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