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Question Number 10184 Answers: 2 Comments: 0

if a_− =2i+3j . b_− =19−15j and c_− =5i−7j. find the value of x such that xa_− + yc_− =b

$${if}\:\underset{−} {{a}}\:=\mathrm{2}{i}+\mathrm{3}{j}\:.\:\underset{−} {{b}}=\mathrm{19}−\mathrm{15}{j}\:{and}\: \\ $$$$\underset{−} {{c}}\:=\mathrm{5}{i}−\mathrm{7}{j}.\:{find}\:{the}\:{value}\:{of}\:{x}\:{such} \\ $$$${that}\:{x}\underset{−} {{a}}\:+\:{y}\underset{−} {{c}}\:={b} \\ $$$$ \\ $$

Question Number 10170 Answers: 1 Comments: 0

y . f(xy) = f(x) x,y ∈ R If f(4) = 1006, so f(2012) = ?

$${y}\:.\:{f}\left({xy}\right)\:=\:{f}\left({x}\right)\:\:\:\:\:\:\:\:{x},\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{4}\right)\:=\:\mathrm{1006},\:\mathrm{so}\:{f}\left(\mathrm{2012}\right)\:=\:? \\ $$

Question Number 10169 Answers: 1 Comments: 0

((2013)/1) + ((2013)/(1+2)) + ((2013)/(1+2+3)) + ... + ((2013)/(1+2+3+...+2012)) = ?

$$\frac{\mathrm{2013}}{\mathrm{1}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+\:...\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{2012}}\:=\:? \\ $$

Question Number 10168 Answers: 0 Comments: 0

If the roots of quadratic equation ax^2 + bx + c = 0 were within the interval [0,1], the maximum value from (((2a−b)(a−b))/(a(a−b+c))) is ...

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\mathrm{were}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[\mathrm{0},\mathrm{1}\right], \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\frac{\left(\mathrm{2}{a}−{b}\right)\left({a}−{b}\right)}{{a}\left({a}−{b}+{c}\right)}\:\:\:\:\mathrm{is}\:... \\ $$

Question Number 10166 Answers: 1 Comments: 1

Question Number 10159 Answers: 1 Comments: 2

Question Number 10157 Answers: 1 Comments: 0

the difference of two number is 3. if the sum of their reciprocal is (7/(10)) . find the numbres

$${the}\:{difference}\:{of}\:{two}\:{number}\:{is}\:\mathrm{3}. \\ $$$${if}\:{the}\:{sum}\:{of}\:{their}\:{reciprocal}\:{is}\: \\ $$$$\frac{\mathrm{7}}{\mathrm{10}}\:.\:{find}\:{the}\:{numbres} \\ $$

Question Number 10155 Answers: 1 Comments: 0

solve for x sin(x) − (√(3cos(x))) = 1

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:−\:\sqrt{\mathrm{3cos}\left(\mathrm{x}\right)}\:=\:\mathrm{1} \\ $$

Question Number 10154 Answers: 0 Comments: 0

The sum of the first term of sequence is given by S_n = 5n^2 − 2n. A sequence U_1 , U_2 , U_3 .... is defined by U_t = S_t − S_(t − 1) . Express U_t in terms of it simplest form. and show that sequences is linear (AP). (a) Find the sum S_n of the n terms of the sequence r^(th ) term is 4 × 2^(−1) (b) The value of n for which the difference between S_n and less than 10^(−4)

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{sequence}\:\mathrm{is}\: \\ $$$$\mathrm{given}\:\mathrm{by}\:\:\mathrm{S}_{\mathrm{n}} \:=\:\mathrm{5n}^{\mathrm{2}} \:−\:\mathrm{2n}.\:\mathrm{A}\:\mathrm{sequence}\:\: \\ $$$$\mathrm{U}_{\mathrm{1}} ,\:\mathrm{U}_{\mathrm{2}} ,\:\mathrm{U}_{\mathrm{3}} \:....\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{U}_{\mathrm{t}} \:=\:\mathrm{S}_{\mathrm{t}} \:−\:\mathrm{S}_{\mathrm{t}\:−\:\mathrm{1}} . \\ $$$$\mathrm{Express}\:\mathrm{U}_{\mathrm{t}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{it}\:\mathrm{simplest}\:\mathrm{form}.\:\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{sequences}\:\mathrm{is}\:\mathrm{linear}\:\left(\mathrm{AP}\right). \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{of}\:\mathrm{the}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{sequence}\:\mathrm{r}^{\mathrm{th}\:} \:\mathrm{term}\:\mathrm{is}\:\mathrm{4}\:×\:\mathrm{2}^{−\mathrm{1}} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{difference} \\ $$$$\mathrm{between}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{less}\:\mathrm{than}\:\mathrm{10}^{−\mathrm{4}} \\ $$

Question Number 10152 Answers: 0 Comments: 0

Question Number 10147 Answers: 0 Comments: 1

∫(√(p/(p−1)))dp=...?

$$\int\sqrt{\frac{\mathrm{p}}{\mathrm{p}−\mathrm{1}}}\mathrm{dp}=...? \\ $$

Question Number 10143 Answers: 2 Comments: 0

x∈Z (x+4)^(x^2 −16) =1 ⇒Σx=?

$$\mathrm{x}\in\mathrm{Z} \\ $$$$\left(\mathrm{x}+\mathrm{4}\right)^{\mathrm{x}^{\mathrm{2}} −\mathrm{16}} =\mathrm{1}\:\:\:\Rightarrow\Sigma\mathrm{x}=? \\ $$

Question Number 10142 Answers: 0 Comments: 3

Question Number 10138 Answers: 1 Comments: 0

2^(x+y) =0.125 (0.125)^(x−y) =2 ⇒ x×y=?

$$\mathrm{2}^{\mathrm{x}+\mathrm{y}} =\mathrm{0}.\mathrm{125} \\ $$$$\left(\mathrm{0}.\mathrm{125}\right)^{\mathrm{x}−\mathrm{y}} =\mathrm{2}\:\Rightarrow\:\mathrm{x}×\mathrm{y}=? \\ $$

Question Number 10137 Answers: 1 Comments: 0

lim_(x→0^+ ) ((sin x^m )/(sin^n x)) n;m ∈Z

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\:\frac{{sin}\:{x}^{{m}} }{{sin}^{{n}} \:{x}}\:\:{n};{m}\:\in\mathbb{Z} \\ $$

Question Number 10136 Answers: 0 Comments: 0

Question Number 10133 Answers: 1 Comments: 0

((1+2^(x−y) )/(1+2^(y−x) ))=4⇒x−y=?

$$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\mathrm{2}^{\mathrm{y}−\mathrm{x}} }=\mathrm{4}\Rightarrow\mathrm{x}−\mathrm{y}=? \\ $$

Question Number 10131 Answers: 1 Comments: 0

2^a =9 27^b =8 ⇒a×b=?

$$\mathrm{2}^{\mathrm{a}} =\mathrm{9} \\ $$$$\mathrm{27}^{\mathrm{b}} =\mathrm{8} \\ $$$$\Rightarrow\mathrm{a}×\mathrm{b}=? \\ $$

Question Number 10124 Answers: 1 Comments: 0

x=4^((−2)^(−1) ) y=(0.4)^(−2) ⇒ 2x+4y=?

$$\mathrm{x}=\mathrm{4}^{\left(−\mathrm{2}\right)^{−\mathrm{1}} } \\ $$$$\mathrm{y}=\left(\mathrm{0}.\mathrm{4}\right)^{−\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{2x}+\mathrm{4y}=? \\ $$

Question Number 10128 Answers: 0 Comments: 0

Question Number 10121 Answers: 0 Comments: 0

tank you

$${tank}\:{you} \\ $$

Question Number 10118 Answers: 1 Comments: 1

Let f:R→R be a function such that f(x)=x^3 +x^2 f′(1)+xf′′(2)+f′′′(3) for x∈R. 1)What is f(1) equal to? 2)What is f′(1) equal to? 3)What is f′′′(10) equal to? For this question consider the following: 1) f(2)=f(1)−f(0) 2)f′′(2)−2f′(1)=12 which is/are correct?

$${Let}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:{be}\:{a}\:{function}\:{such}\:{that} \\ $$$${f}\left({x}\right)={x}^{\mathrm{3}} +{x}^{\mathrm{2}} {f}'\left(\mathrm{1}\right)+{xf}''\left(\mathrm{2}\right)+{f}'''\left(\mathrm{3}\right) \\ $$$${for}\:{x}\in\mathbb{R}. \\ $$$$\left.\mathrm{1}\right){What}\:{is}\:{f}\left(\mathrm{1}\right)\:{equal}\:{to}? \\ $$$$\left.\mathrm{2}\right){What}\:{is}\:{f}'\left(\mathrm{1}\right)\:{equal}\:{to}? \\ $$$$\left.\mathrm{3}\right){What}\:{is}\:{f}'''\left(\mathrm{10}\right)\:{equal}\:{to}? \\ $$$${For}\:{this}\:{question}\:{consider}\:{the}\:{following}: \\ $$$$\left.\mathrm{1}\right)\:{f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}\right)−{f}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){f}''\left(\mathrm{2}\right)−\mathrm{2}{f}'\left(\mathrm{1}\right)=\mathrm{12} \\ $$$${which}\:{is}/{are}\:{correct}? \\ $$

Question Number 10117 Answers: 0 Comments: 1

A point is chosen at random inside a rectangle measuring 5 inches by 6 inches.What is the probability that the randomly selected point is at least 1 inch from the edge of rectangle?

$${A}\:{point}\:{is}\:{chosen}\:{at}\:{random}\:{inside} \\ $$$${a}\:{rectangle}\:{measuring}\:\mathrm{5}\:{inches} \\ $$$${by}\:\mathrm{6}\:{inches}.{What}\:{is}\:{the}\:{probability} \\ $$$${that}\:{the}\:{randomly}\:{selected}\:{point} \\ $$$${is}\:{at}\:{least}\:\mathrm{1}\:{inch}\:{from}\:{the}\:{edge}\:{of} \\ $$$${rectangle}? \\ $$

Question Number 10116 Answers: 0 Comments: 1

what is the probability of 5 sundays in the month of december?

$${what}\:{is}\:{the}\:{probability}\:{of}\:\mathrm{5}\:{sundays} \\ $$$${in}\:{the}\:{month}\:{of}\:{december}? \\ $$

Question Number 10114 Answers: 1 Comments: 0

how can demontred tan 3x=_( ) ((3tanx−tan^3 x)/(1_ −3tan^2 x)) pleace help me

$${how}\:{can}\:{demontred} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}\underset{\:\:\:\:\:\:\:\:\:} {=}\frac{\mathrm{3}{tanx}−{tan}^{\mathrm{3}} {x}}{\underset{} {\mathrm{1}}−\mathrm{3}{tan}^{\mathrm{2}} {x}} \\ $$$${pleace}\:{help}\:{me} \\ $$

Question Number 10108 Answers: 1 Comments: 0

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