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Question Number 76465 Answers: 1 Comments: 0

∫e^(−x) (−e^(−3x) +5e^(−2x) −6)sin(2e^(−x) )dx

$$\int{e}^{−{x}} \left(−{e}^{−\mathrm{3}{x}} +\mathrm{5}{e}^{−\mathrm{2}{x}} −\mathrm{6}\right){sin}\left(\mathrm{2}{e}^{−{x}} \right){dx} \\ $$

Question Number 76462 Answers: 1 Comments: 4

∫cos3x e^(−2x) dx

$$\int{cos}\mathrm{3}{x}\:{e}^{−\mathrm{2}{x}} {dx} \\ $$

Question Number 76455 Answers: 1 Comments: 2

In a triangle whose sides measure 5 cm, 6 cm, and 7 cm a point P, inside the triangle is 2 cm from de long side 5 cm and 3 cm from the long side 6 cm. What is the distance from P beside 7 cm side?

$${In}\:{a}\:{triangle}\:{whose}\:{sides}\:{measure} \\ $$$$\mathrm{5}\:{cm},\:\mathrm{6}\:{cm},\:{and}\:\:\mathrm{7}\:{cm}\:{a}\:{point}\:{P},\:{inside} \\ $$$${the}\:{triangle}\:{is}\:\mathrm{2}\:{cm}\:{from}\:{de}\:{long}\:{side} \\ $$$$\mathrm{5}\:{cm}\:{and}\:\mathrm{3}\:{cm}\:{from}\:{the}\:{long}\:{side} \\ $$$$\mathrm{6}\:{cm}.\:{What}\:{is}\:{the}\:{distance}\:{from}\:{P} \\ $$$${beside}\:\mathrm{7}\:{cm}\:{side}? \\ $$

Question Number 76445 Answers: 0 Comments: 6

how evaluate lim_(x→0) (((1−(√(1+x^2 ))×cos x)/x^4 )).

$${how}\:{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }×\mathrm{cos}\:{x}}{{x}^{\mathrm{4}} }\right). \\ $$

Question Number 76443 Answers: 1 Comments: 0

Question Number 76442 Answers: 1 Comments: 0

Question Number 76439 Answers: 1 Comments: 0

solve in [0;2π[ 1+2sin3x≤0

$$\mathrm{solve}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\left[\:\right.\right. \\ $$$$\mathrm{1}+\mathrm{2sin3}{x}\leqslant\mathrm{0} \\ $$

Question Number 76438 Answers: 1 Comments: 0

given N =(4/(((√5)+1)(5^(1/4) +1)(5^(1/8) +1)(5^(1/(16)) +1))) find value of (N+1)^(48) .

$${given}\:{N}\:=\frac{\mathrm{4}}{\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{4}}} +\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{8}}} +\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{16}}} +\mathrm{1}\right)} \\ $$$${find}\:{value}\:{of}\:\left({N}+\mathrm{1}\right)^{\mathrm{48}} . \\ $$

Question Number 76436 Answers: 2 Comments: 0

Question Number 76434 Answers: 2 Comments: 0

if sec x − tan x = 4, then find sin x.

$$\mathrm{if}\:\mathrm{sec}\:\mathrm{x}\:−\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{4},\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\mathrm{sin}\:\mathrm{x}. \\ $$

Question Number 76431 Answers: 1 Comments: 1

how to find x^(2048) + x^(−2048) if x+x^(−1) =(((√5)+1)/2)

$${how}\:{to}\:{find}\:{x}^{\mathrm{2048}} \:+\:{x}^{−\mathrm{2048}} \\ $$$${if}\:\:{x}+{x}^{−\mathrm{1}} =\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 76428 Answers: 2 Comments: 0

Question Number 76424 Answers: 1 Comments: 1

how to calculate ∫(√(x/(√(x/(√(x/(√(...)))))))) dx ?

$${how}\:{to}\:{calculate}\:\int\sqrt{\frac{{x}}{\sqrt{\frac{{x}}{\sqrt{\frac{{x}}{\sqrt{...}}}}}}}\:\:{dx}\:? \\ $$

Question Number 76407 Answers: 0 Comments: 0

Question Number 76404 Answers: 0 Comments: 2

Hello have nice end of year good bless you all i respond note in y re message becsuse i have so many problemes that mack me feel no pleasur any more to do somthing i think its importante to say it i will back Soon i hop so Sorry for my English

$$\mathrm{Hello}\:\mathrm{have}\:\mathrm{nice}\:\mathrm{end}\:\mathrm{of}\:\mathrm{year}\:\mathrm{good}\:\mathrm{bless}\:\mathrm{you} \\ $$$$\mathrm{all}\:\mathrm{i}\:\mathrm{respond}\:\mathrm{note}\:\mathrm{in}\:\mathrm{y}\:\mathrm{re}\:\mathrm{message}\:\mathrm{becsuse}\:\mathrm{i}\:\mathrm{have}\:\mathrm{so}\:\mathrm{many}\:\mathrm{problemes} \\ $$$$\mathrm{that}\:\mathrm{mack}\:\mathrm{me}\:\mathrm{feel}\:\mathrm{no}\:\mathrm{pleasur}\:\mathrm{any}\:\mathrm{more}\:\mathrm{to}\:\mathrm{do}\:\mathrm{somthing} \\ $$$$\mathrm{i}\:\mathrm{think}\:\mathrm{its}\:\mathrm{importante}\:\mathrm{to}\:\mathrm{say}\:\mathrm{it}\:\mathrm{i}\:\mathrm{will}\:\mathrm{back}\:\mathrm{Soon}\:\mathrm{i}\:\mathrm{hop}\:\mathrm{so}\:\:\mathrm{Sorry}\:\mathrm{for} \\ $$$$\mathrm{my}\:\mathrm{English} \\ $$

Question Number 76401 Answers: 1 Comments: 0

In a quadratic equation ax^2 −bx+c=0, a,b, c are distinct primes and the product of the sum of the roots and product of the roots is ((91)/9) . Find the absolute value of difference between the sum of the roots and the product of the roots.

Question Number 76397 Answers: 0 Comments: 2

solve for z∈C [z=a+bi; z^ =a−bi; r∈R] (√(r^2 −z^2 ))=z^ (√(r^2 +z^2 ))=z^

$$\mathrm{solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$$\left[{z}={a}+{b}\mathrm{i};\:\bar {{z}}={a}−{b}\mathrm{i};\:{r}\in\mathbb{R}\right] \\ $$$$\sqrt{{r}^{\mathrm{2}} −{z}^{\mathrm{2}} }=\bar {{z}} \\ $$$$\sqrt{{r}^{\mathrm{2}} +{z}^{\mathrm{2}} }=\bar {{z}} \\ $$

Question Number 76386 Answers: 1 Comments: 2

Are give two parallel lines and a point A is given between them, and the distance from A to the lines are a and b. Determine the cathetus of right−angled triangle in A knowing that the other vertices belong to the parallel lines and the area of the triangle is equal to k^2 .

$${Are}\:{give}\:{two}\:{parallel}\:{lines}\:{and}\:{a}\:{point} \\ $$$${A}\:{is}\:{given}\:{between}\:{them},\:{and}\:{the} \\ $$$${distance}\:{from}\:{A}\:{to}\:{the}\:{lines}\:{are}\: \\ $$$$\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}.\:{Determine}\:{the}\:{cathetus}\:{of} \\ $$$${right}−{angled}\:{triangle}\:{in}\:{A}\:{knowing} \\ $$$${that}\:{the}\:{other}\:{vertices}\:{belong}\:{to} \\ $$$${the}\:{parallel}\:{lines}\:{and}\:{the}\:{area}\:{of} \\ $$$${the}\:{triangle}\:{is}\:{equal}\:{to}\:\boldsymbol{{k}}^{\mathrm{2}} . \\ $$

Question Number 76384 Answers: 0 Comments: 1

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Question Number 76368 Answers: 3 Comments: 5

prove that 1. Σ_(r=1) ^n r = (1/2)n(n+1) 2. Σ_(r=1) ^n r^2 = (1/6)n(n+1)(2n + 1) 3. Σ_(r=1) ^n r^3 = (1/4)n^2 (n + 1)^2

$${prove}\:{that} \\ $$$$\mathrm{1}.\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{r}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right) \\ $$$$\mathrm{2}.\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{r}^{\mathrm{2}} \:=\:\frac{\mathrm{1}}{\mathrm{6}}{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}\:+\:\mathrm{1}\right) \\ $$$$\mathrm{3}.\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{r}^{\mathrm{3}} =\:\frac{\mathrm{1}}{\mathrm{4}}{n}^{\mathrm{2}} \left({n}\:+\:\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 76367 Answers: 0 Comments: 4

prove that Σ_(r=1) ^∞ (1/r^2 ) = (π^2 /6)

$${prove}\:{that}\:\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 76361 Answers: 1 Comments: 3

let A = (((1 1)),((1 1)) ) 1) calculate A^n 2) find e^A ,e^(−A) 3) find sinA and cosA 4) find ch(A) and sh(A)

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:\:,{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{sinA}\:{and}\:{cosA} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{ch}\left({A}\right)\:{and}\:{sh}\left({A}\right) \\ $$