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AllQuestion and Answers: Page 1964

Question Number 11050 Answers: 1 Comments: 0

The function f(x)=acosx+b where a<0 has a maximum value of 8 and a minimum value of −2.Find a+b.

$${The}\:{function}\:{f}\left({x}\right)={acosx}+{b}\:{where} \\ $$$${a}<\mathrm{0}\:{has}\:{a}\:{maximum}\:{value}\:{of}\:\mathrm{8}\:{and} \\ $$$${a}\:{minimum}\:{value}\:{of}\:−\mathrm{2}.\boldsymbol{{F}}{ind}\:{a}+{b}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 11049 Answers: 1 Comments: 1

If n^2 + 3n + 1 is divisible by 3n + 10 Find out all possible solution for n

$$\mathrm{If}\:\:{n}^{\mathrm{2}} \:+\:\mathrm{3}{n}\:+\:\mathrm{1}\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}{n}\:+\:\mathrm{10} \\ $$$$\mathrm{Find}\:\mathrm{out}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution}\:\mathrm{for}\:{n}\: \\ $$

Question Number 11048 Answers: 4 Comments: 0

Which one is largest? (without using calculator) 31^(11) or 17^(14) ??

$$\mathrm{Which}\:\mathrm{one}\:\mathrm{is}\:\mathrm{largest}?\:\left(\mathrm{without}\:\mathrm{using}\:\mathrm{calculator}\right) \\ $$$$\mathrm{31}^{\mathrm{11}} \:\mathrm{or}\:\mathrm{17}^{\mathrm{14}} \:\:?? \\ $$

Question Number 11042 Answers: 1 Comments: 0

∫cos(x)(√(((sin(x)+1)/(sin(x)−1)) )) dx

$$\int{cos}\left({x}\right)\sqrt{\frac{{sin}\left({x}\right)+\mathrm{1}}{{sin}\left({x}\right)−\mathrm{1}}\:}\:{dx} \\ $$

Question Number 11040 Answers: 0 Comments: 0

Question Number 11036 Answers: 2 Comments: 1

li_(n→∼) m Σ_(k=1) ^n ((8n^2 )/(n^4 +1)) =....?

$${l}\underset{{n}\rightarrow\sim} {{i}m}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{8}{n}^{\mathrm{2}} }{{n}^{\mathrm{4}} +\mathrm{1}}\:=....? \\ $$

Question Number 11035 Answers: 1 Comments: 0

A= [(1,(−1)),((−4),(−2)) ] A^(2016) =.....?

$${A}=\begin{bmatrix}{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{4}}&{−\mathrm{2}}\end{bmatrix} \\ $$$${A}^{\mathrm{2016}} =.....? \\ $$

Question Number 11034 Answers: 0 Comments: 1

u= [(1,(−1),2) ] A= [(3,2),(1,3),(0,1) ] v= [(2,(−1)) ] uAv^t =....?

$${u}=\begin{bmatrix}{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{2}}\end{bmatrix} \\ $$$${A}=\begin{bmatrix}{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{1}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix} \\ $$$${v}=\begin{bmatrix}{\mathrm{2}}&{−\mathrm{1}}\end{bmatrix} \\ $$$${uAv}^{{t}} =....? \\ $$

Question Number 11214 Answers: 1 Comments: 0

Question Number 11212 Answers: 1 Comments: 0

Question Number 11217 Answers: 0 Comments: 0

∃e_i :i∈N e_i is a basis vector A∈C^n A=Σ_(i∈N) e_i A_i = ((A_1 ),(A_2 ),(⋮),(A_n ) ) = ∣A⟩ ⟨B∣=(∣B^∗ ⟩)^T ∣A⟩⟨B∣=???

$$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\mid{A}\rangle\langle{B}\mid=??? \\ $$

Question Number 11215 Answers: 0 Comments: 0

Question Number 11024 Answers: 1 Comments: 0

P(x+1)×P(x−1)=4x^2 +8x+a−5 a=?

$${P}\left({x}+\mathrm{1}\right)×{P}\left({x}−\mathrm{1}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{8}{x}+{a}−\mathrm{5} \\ $$$${a}=? \\ $$

Question Number 11023 Answers: 1 Comments: 0

(x^3 +6)×P(x)+6x=ax^3 +2ax+b+3 ⇒b=?

$$\left({x}^{\mathrm{3}} +\mathrm{6}\right)×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}} +\mathrm{2}{ax}+{b}+\mathrm{3} \\ $$$$\Rightarrow{b}=? \\ $$

Question Number 11019 Answers: 2 Comments: 0

Question Number 11020 Answers: 2 Comments: 0

Question Number 11013 Answers: 0 Comments: 0

Euler vs. Newton

$$\mathrm{Euler}\:\mathrm{vs}.\:\mathrm{Newton} \\ $$

Question Number 11011 Answers: 2 Comments: 0

if tan(xy)=x then (dy/dx)=

$${if}\:{tan}\left({xy}\right)={x}\:{then}\:\frac{{dy}}{{dx}}= \\ $$

Question Number 11009 Answers: 1 Comments: 0

If x^3 = y^3 Is it always true that x = y ?

$$\mathrm{If}\:\:{x}^{\mathrm{3}} \:=\:{y}^{\mathrm{3}} \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{always}\:\mathrm{true}\:\mathrm{that}\:{x}\:=\:{y}\:? \\ $$

Question Number 11005 Answers: 1 Comments: 0

prove that (9/4) < (log _2 3)^2 < ((25)/9) .

$${prove}\:{that}\:\frac{\mathrm{9}}{\mathrm{4}}\:<\:\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{3}\right)^{\mathrm{2}} \:<\:\frac{\mathrm{25}}{\mathrm{9}}\:\:. \\ $$

Question Number 10995 Answers: 1 Comments: 1

Prove that 3>(log_2 3)^2 >2.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{3}>\left(\mathrm{log}_{\mathrm{2}} \mathrm{3}\right)^{\mathrm{2}} >\mathrm{2}. \\ $$

Question Number 10994 Answers: 0 Comments: 3

Γ(2407) = (2406)! = ∫_0 ^∞ e^(−x) x^(2406) dx How evaluate ∫e^(−x) x^(2406) dx ???

$$\Gamma\left(\mathrm{2407}\right)\:=\:\left(\mathrm{2406}\right)!\:=\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {x}^{\mathrm{2406}} \:\mathrm{dx} \\ $$$$\mathrm{How}\:\mathrm{evaluate}\:\int{e}^{−{x}} {x}^{\mathrm{2406}} \:\mathrm{dx}\:??? \\ $$

Question Number 10989 Answers: 1 Comments: 0

find the image of the point(5,2) under a rotation of 90° clockwise

$${find}\:{the}\:{image}\:{of}\:{the}\:{point}\left(\mathrm{5},\mathrm{2}\right)\: \\ $$$${under}\:{a}\:{rotation}\:{of}\:\mathrm{90}°\:{clockwise} \\ $$

Question Number 10987 Answers: 1 Comments: 0

If • f(2x + 1) + g(3 − x) = x • f(((3x + 5)/( x + 1))) + 2g(((2x + 1)/(x + 1))) = (x/(x + 1)) for every x ∈ R, x ≠ −1 Find f(x) !!

$$\mathrm{If}\: \\ $$$$\bullet\:{f}\left(\mathrm{2}{x}\:+\:\mathrm{1}\right)\:+\:{g}\left(\mathrm{3}\:−\:{x}\right)\:=\:{x} \\ $$$$\bullet\:{f}\left(\frac{\mathrm{3}{x}\:+\:\mathrm{5}}{\:{x}\:+\:\mathrm{1}}\right)\:+\:\mathrm{2}{g}\left(\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{{x}\:+\:\mathrm{1}}\right)\:=\:\frac{{x}}{{x}\:+\:\mathrm{1}} \\ $$$$\mathrm{for}\:\mathrm{every}\:{x}\:\in\:\mathbb{R},\:\:{x}\:\neq\:−\mathrm{1} \\ $$$$\mathrm{Find}\:{f}\left({x}\right)\:!! \\ $$

Question Number 10981 Answers: 1 Comments: 1

Question Number 10970 Answers: 1 Comments: 0

x^x^x^⋰^2 = 2 What is the value of x ?

$${x}^{{x}^{{x}^{\iddots^{\mathrm{2}} } } } \:=\:\mathrm{2} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$

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