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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^

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

Question Number 10856 Answers: 1 Comments: 0

Find all the solution that fulfilled the equation below (1 + (1/x))^(x + 1) = (1 + (1/(2013)))^(2013)

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{that}\:\mathrm{fulfilled}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{below} \\ $$$$\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)^{{x}\:+\:\mathrm{1}} \:=\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2013}}\right)^{\mathrm{2013}} \\ $$

Question Number 10855 Answers: 1 Comments: 0

(3/(1!+2!+3!)) + (4/(2!+3!+4!)) + (5/(3!+4!+5!)) + ... + ((2016)/(2014!+2015!+2016!)) = ?

$$\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}\:+\:\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}\:+\:\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}\:+\:...\:+\:\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!}\:=\:? \\ $$

Question Number 10854 Answers: 1 Comments: 0

f : R → R f(x . f(x) + f(y)) = (f(x))^2 + y x,y ∈ R f(x) = ??

$${f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$${f}\left({x}\:.\:{f}\left({x}\right)\:+\:{f}\left({y}\right)\right)\:=\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \:+\:{y}\:\:\:\:\:\:\:\:\:\:{x},{y}\:\in\:\mathbb{R} \\ $$$$ \\ $$$${f}\left({x}\right)\:=\:?? \\ $$

Question Number 10853 Answers: 1 Comments: 0

(x + y)^n = Σ_(k=0) ^n ((n),(k) )x^k y^(n−k) (x − y)^n = ???????

$$\left({x}\:+\:{y}\right)^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}{x}^{{k}} {y}^{{n}−{k}} \\ $$$$\left({x}\:−\:{y}\right)^{{n}} \:=\:??????? \\ $$

Question Number 10849 Answers: 0 Comments: 0

Given that f(x) = f(x + 1000) for every x ∈ R If ∫_0 ^3 f(x) = 30,what is the value of ∫_3 ^5 f(x + 2016) dx ?

$$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{1000}\right)\:\mathrm{for}\:\mathrm{every}\:{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:{f}\left({x}\right)\:=\:\mathrm{30},\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{3}} {\overset{\mathrm{5}} {\int}}\:{f}\left({x}\:+\:\mathrm{2016}\right)\:{dx}\:? \\ $$

Question Number 10846 Answers: 1 Comments: 0

Two parallel chords of length 24 cm and 10 cm which lies on opposite sides of a circle are 17 cm apart. Calculate the radius of the circle to the nearest whole number.

$$\mathrm{Two}\:\mathrm{parallel}\:\mathrm{chords}\:\mathrm{of}\:\mathrm{length}\:\mathrm{24}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{10}\:\mathrm{cm}\:\mathrm{which}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{opposite} \\ $$$$\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{17}\:\mathrm{cm}\:\mathrm{apart}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Question Number 10837 Answers: 1 Comments: 0

given that sinA=((12)/(13))and sinB=(4/5), where A and B are acute angles, find cos(A−B) and sin(A+B)

$${given}\:{that}\:{sinA}=\frac{\mathrm{12}}{\mathrm{13}}{and}\:{sinB}=\frac{\mathrm{4}}{\mathrm{5}}, \\ $$$${where}\:{A}\:{and}\:{B}\:{are}\:{acute}\:{angles}, \\ $$$${find}\:{cos}\left({A}−{B}\right)\:{and}\:{sin}\left({A}+{B}\right) \\ $$$$ \\ $$

Question Number 10830 Answers: 2 Comments: 0

lim_(x→∞) ((3^x − 3^(−x) )/(3^x + 3^(−x) ))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{3}^{−\mathrm{x}} }{\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{3}^{−\mathrm{x}} } \\ $$

Question Number 10825 Answers: 1 Comments: 0

Given that sin(x) − sin(y) = sin(θ) cos(x) + cos(y) = cos(θ) Show that cos(x + y) = −(1/2)

$$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:−\:\mathrm{sin}\left(\mathrm{y}\right)\:=\:\mathrm{sin}\left(\theta\right) \\ $$$$\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{y}\right)\:=\:\mathrm{cos}\left(\theta\right) \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cos}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 10820 Answers: 1 Comments: 0