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Question Number 137383 Answers: 3 Comments: 0

What is the remainder 13^(163) when divided by 99

$${What}\:{is}\:{the}\:{remainder}\:\mathrm{13}^{\mathrm{163}} \:{when} \\ $$$${divided}\:{by}\:\mathrm{99}\: \\ $$

Question Number 137382 Answers: 2 Comments: 1

The solution set of equation cos^2 x+cos^2 2x+cos^2 3x = 1 on 0≤x≤2π

$${The}\:{solution}\:{set}\:{of}\:{equation} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{3}{x}\:=\:\mathrm{1}\: \\ $$$${on}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$

Question Number 137379 Answers: 3 Comments: 0

Question Number 137378 Answers: 2 Comments: 0

Given ∫^( x) _0 f(t) dt = x^2 sin (πx) find f(2).

$${Given}\:\underset{\mathrm{0}} {\int}^{\:{x}} {f}\left({t}\right)\:{dt}\:=\:{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\pi{x}\right) \\ $$$${find}\:{f}\left(\mathrm{2}\right). \\ $$

Question Number 137376 Answers: 1 Comments: 0

1+(1/3)+(1/5)+(1/9)+(1/(15))+(1/(25))+...+(1/(45))+(1/(75))+... =?

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{25}}+...+\frac{\mathrm{1}}{\mathrm{45}}+\frac{\mathrm{1}}{\mathrm{75}}+...\:=? \\ $$

Question Number 137374 Answers: 1 Comments: 0

Question Number 137366 Answers: 2 Comments: 0

Find the solution of equation sin^2 x+sin^2 2x+sin^2 3x = 1 on interval (0,2π)

$${Find}\:{the}\:{solution}\:{of}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{3}{x}\:=\:\mathrm{1} \\ $$$${on}\:{interval}\:\left(\mathrm{0},\mathrm{2}\pi\right) \\ $$

Question Number 137365 Answers: 2 Comments: 0

Given f(x^2 +x)+2f(x^2 −3x+2)= 9x^2 −15x find the value of f(2017).

$${Given}\:{f}\left({x}^{\mathrm{2}} +{x}\right)+\mathrm{2}{f}\left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)=\:\mathrm{9}{x}^{\mathrm{2}} −\mathrm{15}{x} \\ $$$${find}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{2017}\right). \\ $$

Question Number 137364 Answers: 3 Comments: 0

Find the remainder 7^(30) divide by 10

$${Find}\:{the}\:{remainder}\:\mathrm{7}^{\mathrm{30}} \:{divide} \\ $$$${by}\:\mathrm{10}\: \\ $$

Question Number 137363 Answers: 2 Comments: 1

As illustrated, the rectangle has an area of 1, and E is the midpoint of AD. BF is one third of AB. What is the area of the shadow?

$$ \\ $$As illustrated, the rectangle has an area of 1, and E is the midpoint of AD. BF is one third of AB. What is the area of the shadow?

Question Number 137359 Answers: 1 Comments: 0

Question Number 137353 Answers: 1 Comments: 0

If 75% of 68 is the same as 85% of n, find n.

$$\mathrm{If}\:\mathrm{75\%}\:\mathrm{of}\:\mathrm{68}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:\mathrm{85\%}\:\mathrm{of}\:\mathrm{n},\:\mathrm{find}\:\mathrm{n}. \\ $$

Question Number 137349 Answers: 0 Comments: 1

Question Number 137347 Answers: 1 Comments: 0

(1/(1+(π^2 /(1+(((π+1)^2 )/(1+(((π+2)^2 )/(1+...))))))))+(1/(1+(((π+1)^2 )/(1+(((π+2)^2 )/(1+...))))))=(1/π) Prove or disprove

$$\frac{\mathrm{1}}{\mathrm{1}+\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}+...}}}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\left(\pi+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}+...}}}=\frac{\mathrm{1}}{\pi}\:\: \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$

Question Number 137345 Answers: 1 Comments: 0

ℓ = ∫_0 ^( π/4) (√(cos^3 (2x))) cos x dx =?

$$\ell\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \sqrt{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)}\:\mathrm{cos}\:{x}\:{dx}\:=?\: \\ $$

Question Number 137341 Answers: 1 Comments: 0

∫ (dx/(e^(x/2) +e^(x/3) +e^(x/6) +1)) =?

$$\int\:\frac{{dx}}{\mathrm{e}^{{x}/\mathrm{2}} +{e}^{{x}/\mathrm{3}} +{e}^{{x}/\mathrm{6}} +\mathrm{1}}\:=? \\ $$

Question Number 137340 Answers: 1 Comments: 0

Question Number 137338 Answers: 1 Comments: 0

Given ((cos 8θ+6cos 6θ+13cos 4θ+8cos 2θ)/(cos 7θ+5cos 5θ+8cos 3θ)) = (1/2) then what the value of tan 2θ ?

$$\mathrm{Given}\:\frac{\mathrm{cos}\:\mathrm{8}\theta+\mathrm{6cos}\:\mathrm{6}\theta+\mathrm{13cos}\:\mathrm{4}\theta+\mathrm{8cos}\:\mathrm{2}\theta}{\mathrm{cos}\:\mathrm{7}\theta+\mathrm{5cos}\:\mathrm{5}\theta+\mathrm{8cos}\:\mathrm{3}\theta}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{2}\theta\:? \\ $$

Question Number 137335 Answers: 1 Comments: 0

P(x) = 3x^75 + 2x^14 - 3x^2 - 1. What is the remainder when the above polynomial of s divided by x^2+x+1?

$$ \\ $$P(x) = 3x^75 + 2x^14 - 3x^2 - 1. What is the remainder when the above polynomial of s divided by x^2+x+1?

Question Number 137332 Answers: 0 Comments: 0

Question Number 137328 Answers: 1 Comments: 0

Question Number 137327 Answers: 1 Comments: 0

in triangle ΔABC: BC=1, ∠B=2∠A. find the maximum area of ΔABC.

$${in}\:{triangle}\:\Delta{ABC}:\:{BC}=\mathrm{1},\:\angle{B}=\mathrm{2}\angle{A}. \\ $$$${find}\:{the}\:{maximum}\:{area}\:{of}\:\Delta{ABC}. \\ $$

Question Number 137324 Answers: 1 Comments: 0

how to evaluate this one : P = (1+ (1/(1958)))(1+ (1/(1959)))(1+ (1/(1960)))...(1+ (1/(2017)))(1+ (1/(2018)))(1+ (1/(2019))) P = ?

$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{evaluate}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{one}}\:: \\ $$$$\mathrm{P}\:=\:\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1958}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1959}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{1960}}\right)...\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2017}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2018}}\right)\left(\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2019}}\right) \\ $$$$\boldsymbol{\mathrm{P}}\:=\:?\: \\ $$

Question Number 137321 Answers: 0 Comments: 0

H(x)=(8/(x−2)) and f(x)=((x^2 +3x+6)/(2x−4)) 1)Calculate the surface V_n of area limited by the the line x=6; x=6+n (n∈N^∗ ) and the curve of H(x) and f(x) in function of n. 2) Knowing that 1^2 +2^2 +...+n^2 =((n(n+1)(2n+1))/6) Deduct the value of S_n =V_1 +V_2 +...+V_(n ) in funtion of n . 3) Determinate the smallest integer n such that S_n >100

$${H}\left({x}\right)=\frac{\mathrm{8}}{{x}−\mathrm{2}}\:{and}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{6}}{\mathrm{2}{x}−\mathrm{4}} \\ $$$$\left.\mathrm{1}\right){Calculate}\:{the}\:{surface}\:{V}_{\boldsymbol{{n}}} \:{of} \\ $$$${area}\:{limited}\:{by}\:{the}\:{the}\:{line} \\ $$$${x}=\mathrm{6};\:{x}=\mathrm{6}+\boldsymbol{{n}}\:\left({n}\in\mathbb{N}^{\ast} \right)\:{and}\:{the} \\ $$$${curve}\:{of}\:{H}\left({x}\right)\:{and}\:{f}\left({x}\right)\:{in}\:{function} \\ $$$${of}\:\boldsymbol{{n}}. \\ $$$$\left.\mathrm{2}\right)\:{Knowing}\:{that}\:\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +...+{n}^{\mathrm{2}} =\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$$${Deduct}\:{the}\:{value}\:{of}\: \\ $$$${S}_{{n}} ={V}_{\mathrm{1}} +{V}_{\mathrm{2}} +...+{V}_{{n}\:} {in}\:{funtion} \\ $$$${of}\:{n}\:. \\ $$$$\left.\mathrm{3}\right)\:{Determinate}\:{the}\:{smallest} \\ $$$${integer}\:{n}\:{such}\:{that}\:{S}_{{n}} >\mathrm{100} \\ $$

Question Number 137317 Answers: 0 Comments: 3

Question Number 137316 Answers: 0 Comments: 0

An alternating current after passing through rectifire has the form i=I_0 sinx for 0≤x≤π =0 for π≤x≤2π where I_0 is the maximum current and period is 2π.express i is a fourire series and evaluate (1/(1.3))+(1/(3.5))+(1/(5.7))+.........∞

$${An}\:{alternating}\:{current}\:{after}\:{passing}\: \\ $$$$\:{through}\:{rectifire}\:{has}\:{the} \\ $$$${form}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{i}={I}_{\mathrm{0}} {sinx}\:\:\:\:\:\:{for}\:\mathrm{0}\leqslant{x}\leqslant\pi \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:\pi\leqslant{x}\leqslant\mathrm{2}\pi \\ $$$${where}\:{I}_{\mathrm{0}} \:{is}\:{the}\:{maximum}\:{current}\: \\ $$$${and}\:{period}\:{is}\:\mathrm{2}\pi.{express}\:{i}\:{is}\:{a}\: \\ $$$${fourire}\:{series}\:{and}\:{evaluate} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}.\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}.\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{7}}+.........\infty \\ $$

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