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Question Number 10933 Answers: 2 Comments: 0

If p and q are the roots for the x^2 − (a + 1)x + (−a − (5/2)) = 0 The minimum value of p^(2 ) + q^2 is ...

$$\mathrm{If}\:\:{p}\:\:\mathrm{and}\:\:{q}\:\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{for}\:\mathrm{the} \\ $$$${x}^{\mathrm{2}} \:−\:\left({a}\:+\:\mathrm{1}\right){x}\:+\:\left(−{a}\:−\:\frac{\mathrm{5}}{\mathrm{2}}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:{p}^{\mathrm{2}\:} +\:{q}^{\mathrm{2}} \:\:\mathrm{is}\:... \\ $$

Question Number 10917 Answers: 1 Comments: 0

hence show that i)((1−cos4θ)/(sin4θ))=tan2θ ii)((1−cos6θ)/(sin6θ))=tan3θ

$${hence}\:{show}\:{that} \\ $$$$\left.{i}\right)\frac{\mathrm{1}−{cos}\mathrm{4}\theta}{{sin}\mathrm{4}\theta}={tan}\mathrm{2}\theta \\ $$$$\left.{ii}\right)\frac{\mathrm{1}−{cos}\mathrm{6}\theta}{{sin}\mathrm{6}\theta}={tan}\mathrm{3}\theta \\ $$

Question Number 10916 Answers: 1 Comments: 0

find all possible values of cosθ such that 2cot^2 θ+cosθ=0

$${find}\:{all}\:{possible}\:{values}\:{of}\:{cos}\theta\:{such} \\ $$$${that}\:\mathrm{2}{cot}^{\mathrm{2}} \theta+{cos}\theta=\mathrm{0} \\ $$

Question Number 10914 Answers: 1 Comments: 0

A 200 N force inclined at 40° above the horizontal , drag load along the horizontal floor. coefficient of the kinetic friction between the load is 0.30 and the load experiences an acceleration of 1.2 m/s^2 , What is the mass of the load.

$$\mathrm{A}\:\mathrm{200}\:\mathrm{N}\:\mathrm{force}\:\mathrm{inclined}\:\mathrm{at}\:\mathrm{40}°\:\mathrm{above}\:\mathrm{the}\:\mathrm{horizontal}\:,\:\mathrm{drag}\:\mathrm{load}\:\mathrm{along}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{floor}.\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{load}\:\mathrm{is}\:\mathrm{0}.\mathrm{30}\: \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{load}\:\mathrm{experiences}\:\mathrm{an}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{1}.\mathrm{2}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} , \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{load}. \\ $$

Question Number 10913 Answers: 1 Comments: 0

∫_( 1) ^( 3) x^x dx

$$\int_{\:\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{x}^{\mathrm{x}} \:\:\mathrm{dx} \\ $$

Question Number 10912 Answers: 0 Comments: 1

5^(log_2 3) is transcendental? General: Let a,b and c algebraic and log_b c transcendental. If a^(log_b c) is algebraic, so b = a^q , with q rational?

$$\mathrm{5}^{\mathrm{log}_{\mathrm{2}} \mathrm{3}} \:\mathrm{is}\:\mathrm{transcendental}? \\ $$$$\mathrm{General}: \\ $$$$\mathrm{Let}\:{a},{b}\:\mathrm{and}\:{c}\:\mathrm{algebraic}\:\mathrm{and}\:\mathrm{log}_{{b}} {c}\: \\ $$$$\mathrm{transcendental}.\:\mathrm{If}\:{a}^{\mathrm{log}_{{b}} {c}} \:\mathrm{is}\:\mathrm{algebraic},\:\mathrm{so} \\ $$$${b}\:=\:{a}^{{q}} ,\:\mathrm{with}\:{q}\:\mathrm{rational}? \\ $$

Question Number 10908 Answers: 1 Comments: 0

Question Number 10907 Answers: 1 Comments: 0

express in partial fraction ((3x+2)/((x^2 −1)(x+1)))

$$\mathrm{express}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$$$\frac{\mathrm{3x}+\mathrm{2}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)} \\ $$

Question Number 10906 Answers: 1 Comments: 1

Q . smallest positive x satisfying the equation sin3x+3cosx=2sin2x(sinx+cosx) , is

$${Q}\:.\:\:{smallest}\:{positive}\:{x}\:{satisfying}\:{the}\:{equation} \\ $$$${sin}\mathrm{3}{x}+\mathrm{3}{cosx}=\mathrm{2}{sin}\mathrm{2}{x}\left({sinx}+{cosx}\right)\:,\:{is} \\ $$

Question Number 10903 Answers: 0 Comments: 0

Question Number 10902 Answers: 2 Comments: 0

∫(√(1−x^2 ))dx=?

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 10900 Answers: 0 Comments: 1

Question Number 10899 Answers: 1 Comments: 0

Question Number 10898 Answers: 1 Comments: 0

Question Number 10887 Answers: 1 Comments: 0

Suppose that f(x) = (1/(x + 1)) and g(x) = (4/(x + 1)) . Find the domain of each of the composition (a) f o g (b) f o f

$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}\:+\:\mathrm{1}}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4}}{\mathrm{x}\:+\:\mathrm{1}}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{composition}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{f}\:\mathrm{o}\:\mathrm{g}\:\:\:\left(\mathrm{b}\right)\:\:\mathrm{f}\:\mathrm{o}\:\mathrm{f} \\ $$

Question Number 10880 Answers: 1 Comments: 0

∫ (x + 3)(√((x + 4))) dx

$$\left.\int\:\left(\mathrm{x}\:+\:\mathrm{3}\right)\sqrt{\left(\mathrm{x}\:+\:\mathrm{4}\right.}\right)\:\mathrm{dx}\: \\ $$

Question Number 10876 Answers: 1 Comments: 0

∫_( 0) ^( 1) ∫_( x) ^( (√x)) (x + y^5 ) dy dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \int_{\:\mathrm{x}} ^{\:\sqrt{\mathrm{x}}} \:\left(\mathrm{x}\:+\:\mathrm{y}^{\mathrm{5}} \right)\:\mathrm{dy}\:\mathrm{dx} \\ $$

Question Number 10889 Answers: 0 Comments: 0

The solution of the Schanuel′s Conjecture will to decide if γ is transcendental or not? Tell me all consequences of the conjecture.

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Schanuel}'\mathrm{s}\:\mathrm{Conjecture} \\ $$$$\mathrm{will}\:\mathrm{to}\:\mathrm{decide}\:\mathrm{if}\:\gamma\:\mathrm{is}\:\mathrm{transcendental}\:\mathrm{or}\:\mathrm{not}? \\ $$$$\mathrm{Tell}\:\mathrm{me}\:\mathrm{all}\:\mathrm{consequences}\:\mathrm{of}\:\mathrm{the}\:\mathrm{conjecture}. \\ $$

Question Number 10874 Answers: 1 Comments: 0

If f(x + 3) = 2x^2 − 3x + 5. find f(5)

$$\mathrm{If}\:\:\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{3}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{5}.\:\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{5}\right) \\ $$

Question Number 10872 Answers: 1 Comments: 0

In a cultural gathering of 400 people, there are 270 men and 200 musicians. Of the latter, 80 are singers. 60 of the women are not musicians and 220 of the men are not singers. How many of the women are musicians but not singers. if there are 150 singers altogether and 40 men are both musicians and singers.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{cultural}\:\mathrm{gathering}\:\mathrm{of}\:\mathrm{400}\:\mathrm{people},\:\mathrm{there}\:\mathrm{are}\:\mathrm{270}\:\mathrm{men}\:\mathrm{and}\:\mathrm{200} \\ $$$$\mathrm{musicians}.\:\mathrm{Of}\:\mathrm{the}\:\mathrm{latter},\:\mathrm{80}\:\mathrm{are}\:\mathrm{singers}.\:\mathrm{60}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are}\:\mathrm{not}\:\:\mathrm{musicians} \\ $$$$\mathrm{and}\:\mathrm{220}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{are}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are} \\ $$$$\mathrm{musicians}\:\mathrm{but}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{150}\:\mathrm{singers}\:\mathrm{altogether}\:\mathrm{and}\: \\ $$$$\mathrm{40}\:\mathrm{men}\:\mathrm{are}\:\mathrm{both}\:\mathrm{musicians}\:\mathrm{and}\:\mathrm{singers}. \\ $$

Question Number 10873 Answers: 1 Comments: 0

without using calculator or table, find the exact value of : sin[tan^(−1) ((1/2))]

$$\mathrm{without}\:\mathrm{using}\:\mathrm{calculator}\:\mathrm{or}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\:: \\ $$$$\mathrm{sin}\left[\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right] \\ $$

Question Number 10868 Answers: 0 Comments: 0

Question Number 10867 Answers: 0 Comments: 0

(1) Show that : ((x^(2n + 1) − y^(2n + 1) )/(x − y)) = x^(2n ) + x^(2n − 1) y + ... + xy^(2n − 1) + y^(2n) (2) Show that: ((x^(2n) − y^(2n) )/(x − y)) = x^(2n − 1 ) + x^(2n − 2) y + ... + xy^(2n − 2) + y^(2n − 1)

$$\left(\mathrm{1}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}\:: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}\:+\:\mathrm{1}} \:−\:\mathrm{y}^{\mathrm{2n}\:+\:\mathrm{1}} }{\mathrm{x}\:−\:\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2n}\:} +\:\mathrm{x}^{\mathrm{2n}\:−\:\mathrm{1}} \mathrm{y}\:+\:...\:+\:\mathrm{xy}^{\mathrm{2n}\:−\:\mathrm{1}} \:+\:\mathrm{y}^{\mathrm{2n}} \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}} \:−\:\mathrm{y}^{\mathrm{2n}} }{\mathrm{x}\:−\:\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2n}\:\:−\:\mathrm{1}\:} +\:\mathrm{x}^{\mathrm{2n}\:−\:\mathrm{2}} \mathrm{y}\:+\:...\:+\:\mathrm{xy}^{\mathrm{2n}\:−\:\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2n}\:−\:\mathrm{1}} \\ $$

Question Number 10865 Answers: 0 Comments: 0

Question Number 10864 Answers: 1 Comments: 0

Question Number 10862 Answers: 2 Comments: 2

Given that: a^ = 3i + 4j + 5k and b^ = 2i + 2j + 3k and c^ = 6i − 7j − 8k. find 3a^ + 2b^ − 3c^

$$\mathrm{Given}\:\mathrm{that}:\:\:\hat {\mathrm{a}}\:=\:\mathrm{3i}\:+\:\mathrm{4j}\:+\:\mathrm{5k}\:\:\mathrm{and}\:\:\hat {\mathrm{b}}\:=\:\mathrm{2i}\:+\:\mathrm{2j}\:+\:\mathrm{3k}\:\:\mathrm{and}\:\:\:\hat {\mathrm{c}}\:=\:\mathrm{6i}\:−\:\mathrm{7j}\:−\:\mathrm{8k}. \\ $$$$\mathrm{find} \\ $$$$\mathrm{3}\hat {\mathrm{a}}\:+\:\mathrm{2}\hat {\mathrm{b}}\:−\:\mathrm{3}\hat {\mathrm{c}} \\ $$

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