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Question Number 11844 Answers: 2 Comments: 0

cotα+cosecα=k then find cosecα−cotα and also find cotα

$$\mathrm{cot}\alpha+\mathrm{cosec}\alpha={k}\:{then}\:{find}\:\mathrm{cosec}\alpha−{cot}\alpha\:{and}\:{also}\:{find}\:{cot}\alpha \\ $$

Question Number 11843 Answers: 1 Comments: 0

Differentiate, ln(cosx) from the first principle.

$$\mathrm{Differentiate},\:\:\mathrm{ln}\left(\mathrm{cosx}\right)\:\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}. \\ $$

Question Number 11838 Answers: 1 Comments: 0

((2^2 +1)/(2^2 −1)) + ((3^2 +1)/(3^2 −1)) + ((4^2 +1)/(4^2 −1)) + .... + ((20^2 +1)/(20^2 −1)) = ....?

$$\frac{\mathrm{2}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2}} −\mathrm{1}}\:+\:\frac{\mathrm{4}^{\mathrm{2}} +\mathrm{1}}{\mathrm{4}^{\mathrm{2}} −\mathrm{1}}\:+\:....\:+\:\frac{\mathrm{20}^{\mathrm{2}} +\mathrm{1}}{\mathrm{20}^{\mathrm{2}} −\mathrm{1}}\:=\:....? \\ $$

Question Number 11834 Answers: 3 Comments: 0

Prove that ∀x,y∈R ⇒7x^2 −6xy+2y^2 +x+3 > 0

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\forall\boldsymbol{{x}},\boldsymbol{{y}}\in\boldsymbol{{R}} \\ $$$$\Rightarrow\mathrm{7}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{xy}}+\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{3}\:>\:\mathrm{0} \\ $$

Question Number 11831 Answers: 0 Comments: 0

the system of equation a − (√(c^2 −(1/(16)) ))= (√(b^2 − (1/(16)))) b − (√(a^2 − (1/(25))))= (√(c^2 − (1/(25)))) c − (√(b^2 − (1/(36))))= (√(a^2 − (1/(36)))) given that a, b, c are real numbers that satisfy they system of equation ... if a + b + c = (x/(√(y ))) where x, y are positive integers and y is square free find the value of x + y

$$\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{a}\:−\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\frac{\mathrm{1}}{\mathrm{16}}\:}=\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{16}}} \\ $$$$\mathrm{b}\:−\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}}=\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}} \\ $$$$\mathrm{c}\:−\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}}=\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}} \\ $$$$ \\ $$$$\mathrm{given}\:\mathrm{that}\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\: \\ $$$$\mathrm{that}\:\mathrm{satisfy}\:\mathrm{they}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:... \\ $$$$\mathrm{if}\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:=\:\frac{\mathrm{x}}{\sqrt{\mathrm{y}\:}}\:\mathrm{where}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\: \\ $$$$\mathrm{positive}\:\mathrm{integers}\:\mathrm{and}\:\mathrm{y}\:\mathrm{is}\:\mathrm{square}\:\mathrm{free} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:+\:\mathrm{y}\: \\ $$$$ \\ $$

Question Number 11828 Answers: 0 Comments: 0

A sample of steam at 140 bar is states to have enthalpy of 3009.1 kJ/kg, Calculate the internal energy and entropy.

$$\mathrm{A}\:\:\mathrm{sample}\:\mathrm{of}\:\mathrm{steam}\:\mathrm{at}\:\mathrm{140}\:\mathrm{bar}\:\mathrm{is}\:\mathrm{states}\:\mathrm{to}\:\mathrm{have}\:\mathrm{enthalpy}\:\mathrm{of}\:\:\mathrm{3009}.\mathrm{1}\:\mathrm{kJ}/\mathrm{kg}, \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{entropy}. \\ $$

Question Number 11827 Answers: 1 Comments: 0

∫x^2 dcosx=?

$$\int\mathrm{x}^{\mathrm{2}} \mathrm{dcosx}=? \\ $$

Question Number 11823 Answers: 1 Comments: 0

3 + 2(3^2 ) + 3(3^3 ) + ... + 10(3^(10) ) = ?

$$\mathrm{3}\:+\:\mathrm{2}\left(\mathrm{3}^{\mathrm{2}} \right)\:+\:\mathrm{3}\left(\mathrm{3}^{\mathrm{3}} \right)\:+\:...\:+\:\mathrm{10}\left(\mathrm{3}^{\mathrm{10}} \right)\:=\:? \\ $$

Question Number 11822 Answers: 1 Comments: 0

∫ ((tan x)/(1 + sin x)) dx

$$\int\:\frac{\mathrm{tan}\:{x}}{\mathrm{1}\:+\:\mathrm{sin}\:{x}}\:{dx} \\ $$

Question Number 11813 Answers: 1 Comments: 3

Question Number 11805 Answers: 2 Comments: 0

x^y = y^x x^2 = y^3 find x and y

$$\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{y}^{\mathrm{x}} \:\:\:\: \\ $$$$\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

Question Number 11801 Answers: 0 Comments: 1

pl show me app?

$$\mathrm{pl}\:\mathrm{show}\:\mathrm{me}\:\mathrm{app}? \\ $$

Question Number 11800 Answers: 1 Comments: 0

Find the sum Σ_(n=1) ^∞ (1/((n + 1)(√n) + n(√(n + 1))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{n}\:+\:\mathrm{1}\right)\sqrt{\mathrm{n}}\:\:+\:\:\mathrm{n}\sqrt{\mathrm{n}\:+\:\mathrm{1}}} \\ $$

Question Number 11799 Answers: 0 Comments: 0

Prove using the density of Q in R that every real number x is the limit of a cauchy sequence of rational numbers (r_n )_(n∈N) . Give a sequence of irrational numbers (S_n ) such that S_n → x.

$$\mathrm{Prove}\:\mathrm{using}\:\mathrm{the}\:\mathrm{density}\:\mathrm{of}\:\boldsymbol{\mathrm{Q}}\:\mathrm{in}\:\mathbb{R}\:\mathrm{that}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:\mathrm{x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{cauchy}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{numbers}\:\left(\mathrm{r}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathrm{N}} .\:\mathrm{Give}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{irrational}\: \\ $$$$\mathrm{numbers}\:\left(\mathrm{S}_{\mathrm{n}} \right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{S}_{\mathrm{n}} \:\rightarrow\:\mathrm{x}. \\ $$

Question Number 11770 Answers: 1 Comments: 0

ax^3 +bx^2 +cx+d=0 pls.solve

$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0}\:{pls}.{solve} \\ $$

Question Number 11769 Answers: 0 Comments: 0

ax^3 +bx^2 +cx+d=0 solve

$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0}\:{solve} \\ $$

Question Number 11768 Answers: 0 Comments: 0

ax^3 +bx^2 +cx+d=0 solve it.

$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0}\:{solve}\:{it}. \\ $$

Question Number 11766 Answers: 1 Comments: 0

∫(1/(sin2x))dx=?

$$\int\frac{\mathrm{1}}{\mathrm{sin2x}}\mathrm{dx}=? \\ $$

Question Number 11764 Answers: 1 Comments: 0

if x y and z are solution of ((x + xy)/(x + y + 1)) = 2 ((2x + xz)/(x + z +2)) = 3 ((2 + 2y+ z + yz)/(y + z +3)) = 4 so, the value of (1/x) + (1/(y + 1)) + (1/(z + 2 )) = ....?

$$\mathrm{if}\:\mathrm{x}\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\mathrm{are}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\frac{\mathrm{x}\:+\:\mathrm{xy}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{2} \\ $$$$\frac{\mathrm{2x}\:+\:\mathrm{xz}}{\mathrm{x}\:+\:\mathrm{z}\:+\mathrm{2}}\:=\:\mathrm{3} \\ $$$$\frac{\mathrm{2}\:+\:\mathrm{2y}+\:\mathrm{z}\:+\:\mathrm{yz}}{\mathrm{y}\:+\:\mathrm{z}\:+\mathrm{3}}\:=\:\mathrm{4} \\ $$$$\mathrm{so},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{z}\:+\:\mathrm{2}\:}\:=\:....? \\ $$$$ \\ $$

Question Number 11759 Answers: 1 Comments: 0

A quadrilateral with consecutive sides of lenght 7, 15, 15, and d is inscribed in a circle with its diameter d. Find the radius of circle

$$\mathrm{A}\:\mathrm{quadrilateral}\:\mathrm{with}\:\mathrm{consecutive}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{7},\:\mathrm{15},\:\mathrm{15},\:\mathrm{and}\:{d} \\ $$$$\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{its}\:\mathrm{diameter}\:{d}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle} \\ $$

Question Number 11791 Answers: 1 Comments: 0

What is the velocity of sound at 100°C if the velocity of sound at 0°C is 340 m/s

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{at}\:\mathrm{100}°\mathrm{C}\:\:\mathrm{if}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{at}\:\mathrm{0}°\mathrm{C}\:\mathrm{is}\:\mathrm{340}\:\mathrm{m}/\mathrm{s} \\ $$

Question Number 11754 Answers: 1 Comments: 0

How many numbers between 1 − 2017 that aren′t divisible by 5, 6, 7, 8 ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{between}\:\mathrm{1}\:−\:\mathrm{2017} \\ $$$$\mathrm{that}\:\mathrm{aren}'\mathrm{t}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{6},\:\mathrm{7},\:\mathrm{8}\:? \\ $$

Question Number 11753 Answers: 2 Comments: 0

a, b, c are the roots from equation x^3 − 5x^2 − 9x + 10 = 0 If P(x) = Ax^3 + Bx^2 + Cx − 2015 and P(a) = b + c P(b) = a + c P(c) = a + b What is the value of A + B + C ?

$${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{from}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{9}{x}\:+\:\mathrm{10}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{P}\left({x}\right)\:=\:{Ax}^{\mathrm{3}} \:+\:{Bx}^{\mathrm{2}} \:+\:{Cx}\:−\:\mathrm{2015}\:\mathrm{and} \\ $$$${P}\left({a}\right)\:=\:{b}\:+\:{c}\: \\ $$$${P}\left({b}\right)\:=\:{a}\:+\:{c} \\ $$$${P}\left({c}\right)\:=\:{a}\:+\:{b} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{A}\:+\:{B}\:+\:{C}\:? \\ $$

Question Number 11751 Answers: 1 Comments: 0

Simplify: sin(6θ)

$$\mathrm{Simplify}:\:\mathrm{sin}\left(\mathrm{6}\theta\right) \\ $$

Question Number 11748 Answers: 1 Comments: 0

Solve simultaneously x^2 + 4y^2 + xy = 6 .............. equation (i) 3x^2 + 8y^2 = 14 .............. equation (ii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{6}\:\:\:\:\:..............\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{8y}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:..............\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 11743 Answers: 1 Comments: 0

9/3(6×4/8)=?

$$\mathrm{9}/\mathrm{3}\left(\mathrm{6}×\mathrm{4}/\mathrm{8}\right)=? \\ $$

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