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Question Number 14030 Answers: 1 Comments: 0

The general solution of equation tan x tan 4x = 1 is (1) (2n + 1)(π/(10)) , n ∈ Z − {n : n = 5k +2; k ∈ Z} (2) (4n − 1)(π/(10)) , n ∈ Z (3) ((nπ)/(10)) , n ∈ Z (4) 2nπ + (π/(10)) , n ∈ Z

$$\mathrm{The}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{tan}\:{x}\:\mathrm{tan}\:\mathrm{4}{x}\:=\:\mathrm{1}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z}\:−\:\left\{{n}\::\:{n}\:=\:\mathrm{5}{k}\:+\mathrm{2};\:{k}\:\in\:{Z}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{4}{n}\:−\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{3}\right)\:\frac{{n}\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$

Question Number 14028 Answers: 0 Comments: 0

Question Number 14025 Answers: 0 Comments: 0

Calculate the maximum number of orders vissible with a diffraction grating of 500 lines per milimitres using light of wavelenght 600nm .

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{orders}\:\mathrm{vissible}\:\mathrm{with}\:\mathrm{a}\:\mathrm{diffraction}\:\mathrm{grating} \\ $$$$\mathrm{of}\:\mathrm{500}\:\mathrm{lines}\:\mathrm{per}\:\mathrm{milimitres}\:\:\mathrm{using}\:\mathrm{light}\:\mathrm{of}\:\mathrm{wavelenght}\:\mathrm{600nm}\:. \\ $$

Question Number 14020 Answers: 1 Comments: 0

Question Number 14016 Answers: 0 Comments: 2

it remains force×distance=ise

$$\mathrm{it}\:\mathrm{remains} \\ $$$$\mathrm{force}×\mathrm{distance}=\mathrm{ise} \\ $$

Question Number 14015 Answers: 0 Comments: 0

Question Number 14014 Answers: 2 Comments: 0

∫cos^n (x) dx please i need workings.

$$\int\mathrm{cos}^{\mathrm{n}} \left(\mathrm{x}\right)\:\:\mathrm{dx} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{workings}. \\ $$

Question Number 14011 Answers: 0 Comments: 1

simplify: ((4 − j5)/(1 + j2))

$$\mathrm{simplify}:\:\:\frac{\mathrm{4}\:−\:\mathrm{j5}}{\mathrm{1}\:+\:\mathrm{j2}} \\ $$

Question Number 14002 Answers: 2 Comments: 0

If (√(−1)) = i, then what is the value of (√i) ?

$$\mathrm{If}\:\sqrt{−\mathrm{1}}\:=\:{i},\:\mathrm{then}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:? \\ $$

Question Number 13998 Answers: 1 Comments: 1

Question Number 13988 Answers: 0 Comments: 3

Question Number 13986 Answers: 0 Comments: 4

Solve the following system of equations. (x^2 /(√x))+((√y)/y^2 )=((1729)/(64)) (y^2 /(√x))−((√y)/x^2 )=((6908)/(81))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system} \\ $$$$\mathrm{of}\:\mathrm{equations}. \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\sqrt{\mathrm{x}}}+\frac{\sqrt{\mathrm{y}}}{\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{1729}}{\mathrm{64}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{y}^{\mathrm{2}} }{\sqrt{\mathrm{x}}}−\frac{\sqrt{\mathrm{y}}}{\mathrm{x}^{\mathrm{2}} }=\frac{\mathrm{6908}}{\mathrm{81}} \\ $$$$ \\ $$

Question Number 13983 Answers: 0 Comments: 2

Question Number 13982 Answers: 2 Comments: 0

Find the root of the equation z^2 − 8(1 − i)z + 63 − 16i = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{z}^{\mathrm{2}} \:−\:\mathrm{8}\left(\mathrm{1}\:−\:\mathrm{i}\right)\mathrm{z}\:+\:\mathrm{63}\:−\:\mathrm{16i}\:=\:\mathrm{0} \\ $$

Question Number 13978 Answers: 1 Comments: 0

Question Number 13977 Answers: 2 Comments: 1

Question Number 13976 Answers: 1 Comments: 0

Solve: x^2 (y + 1) + y^2 (x − 1)y′ = 0

$$\mathrm{Solve}: \\ $$$$\mathrm{x}^{\mathrm{2}} \left(\mathrm{y}\:+\:\mathrm{1}\right)\:+\:\mathrm{y}^{\mathrm{2}} \left(\mathrm{x}\:−\:\mathrm{1}\right)\mathrm{y}'\:=\:\mathrm{0} \\ $$

Question Number 13965 Answers: 1 Comments: 0

A cathode ray beam is bent in a circle of radius 2cm by uniform field with B = 4.5 × 10^(−3) T. What is the speed of the electrons ??.

$$\mathrm{A}\:\mathrm{cathode}\:\mathrm{ray}\:\mathrm{beam}\:\mathrm{is}\:\mathrm{bent}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\:\mathrm{2cm}\:\mathrm{by}\:\mathrm{uniform}\:\mathrm{field}\:\mathrm{with} \\ $$$$\mathrm{B}\:=\:\mathrm{4}.\mathrm{5}\:×\:\mathrm{10}^{−\mathrm{3}} \:\mathrm{T}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electrons}\:??. \\ $$

Question Number 13960 Answers: 1 Comments: 0

∫_( 0) ^( (a/2)) x^2 (a^2 − x^2 )^(−3/2) dx

$$\int_{\:\:\:\mathrm{0}} ^{\:\frac{\mathrm{a}}{\mathrm{2}}} \:\:\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{x}^{\mathrm{2}} \right)^{−\mathrm{3}/\mathrm{2}} \:\:\mathrm{dx} \\ $$

Question Number 13955 Answers: 0 Comments: 2

y(x)= { ((4+6x−3x^2 ; x < 2)),((2x^2 −14x+20 ; x ≥ 2)) :} Is the function y(x) differentiable with respect to x at x=2 ?

$${y}\left({x}\right)=\begin{cases}{\mathrm{4}+\mathrm{6}{x}−\mathrm{3}{x}^{\mathrm{2}} \:\:\:\:\:\:\:;\:\:{x}\:<\:\mathrm{2}}\\{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{14}{x}+\mathrm{20}\:\:;\:\:{x}\:\geqslant\:\mathrm{2}}\end{cases} \\ $$$${Is}\:{the}\:{function}\:{y}\left({x}\right)\: \\ $$$${differentiable}\:{with}\:{respect}\:{to}\:{x} \\ $$$${at}\:{x}=\mathrm{2}\:? \\ $$

Question Number 13942 Answers: 1 Comments: 0

for v= [(y),(x) ], v∈R^2 v has basis vectors i^ and j^ Assume we apply a basis transform to obtain new basis vectors i^ ′ and j^ ′ What is the new v′?

$$\mathrm{for}\:\:\boldsymbol{{v}}=\begin{bmatrix}{{y}}\\{{x}}\end{bmatrix},\:\:\:\:\boldsymbol{{v}}\in\mathbb{R}^{\mathrm{2}} \\ $$$$\boldsymbol{{v}}\:\mathrm{has}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}\:\mathrm{and}\:\hat {{j}} \\ $$$$\: \\ $$$$\mathrm{Assume}\:\mathrm{we}\:\mathrm{apply}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{transform}\:\mathrm{to} \\ $$$$\mathrm{obtain}\:\mathrm{new}\:\mathrm{basis}\:\mathrm{vectors}\:\hat {{i}}'\:\mathrm{and}\:\hat {{j}}' \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{new}\:\boldsymbol{{v}}'? \\ $$

Question Number 13934 Answers: 0 Comments: 0

Question Number 13929 Answers: 1 Comments: 0

prove for real x,y and a that (√((x+a)^2 +y^2 ))+(√((x−a)^2 +y^2 ))≥2(√(x^2 +y^2 )) .

$${prove}\:{for}\:{real}\:\boldsymbol{{x}},\boldsymbol{{y}}\:{and}\:\boldsymbol{{a}}\:{that} \\ $$$$\sqrt{\left(\boldsymbol{{x}}+\boldsymbol{{a}}\right)^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }+\sqrt{\left(\boldsymbol{{x}}−\boldsymbol{{a}}\right)^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }\geqslant\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:. \\ $$$$ \\ $$

Question Number 13909 Answers: 4 Comments: 5

Solve simutaneously. x(√x) + y(√y) = 183 x(√y) + y(√x) = 185

$$\mathrm{Solve}\:\mathrm{simutaneously}. \\ $$$$\mathrm{x}\sqrt{\mathrm{x}}\:+\:\mathrm{y}\sqrt{\mathrm{y}}\:=\:\mathrm{183} \\ $$$$\mathrm{x}\sqrt{\mathrm{y}}\:+\:\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{185} \\ $$

Question Number 13904 Answers: 2 Comments: 0

Show that : sin(50) + sin(40) = (√2) cos(5)

$$\mathrm{Show}\:\mathrm{that}\:\::\:\:\mathrm{sin}\left(\mathrm{50}\right)\:+\:\mathrm{sin}\left(\mathrm{40}\right)\:=\:\sqrt{\mathrm{2}}\:\mathrm{cos}\left(\mathrm{5}\right) \\ $$

Question Number 13903 Answers: 2 Comments: 1

Find the values of x in the range 0° to 360° for which sin(3x)sin(x) = 2cos(2x) + 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{range}\:\mathrm{0}°\:\mathrm{to}\:\mathrm{360}°\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{sin}\left(\mathrm{3x}\right)\mathrm{sin}\left(\mathrm{x}\right)\:=\:\mathrm{2cos}\left(\mathrm{2x}\right)\:+\:\mathrm{1} \\ $$

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