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AllQuestion and Answers: Page 439

Question Number 175547 Answers: 2 Comments: 0

Question Number 175544 Answers: 1 Comments: 1

tan^6 (10°)+tan^6 (50°)+tan^6 (70°)=?

$$\:\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{10}°\right)+\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{50}°\right)+\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{70}°\right)=? \\ $$

Question Number 175531 Answers: 2 Comments: 0

∫ (dt/(5cos t+6sin t)) =?

$$\:\int\:\frac{{dt}}{\mathrm{5cos}\:{t}+\mathrm{6sin}\:{t}}\:=? \\ $$

Question Number 175511 Answers: 0 Comments: 1

Question Number 175516 Answers: 1 Comments: 0

Question Number 175505 Answers: 1 Comments: 2

N=64990691606209 is a semi-prime number. That is, N=pq where p and q are prime numbers. Find p and q:

$${N}=\mathrm{64990691606209}\:\mathrm{is}\:\mathrm{a}\:\mathrm{semi}-\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{That}\:\mathrm{is},\:{N}={pq}\:\mathrm{where}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{prime}\:\mathrm{numbers}. \\ $$$$\mathrm{Find}\:{p}\:\mathrm{and}\:{q}: \\ $$

Question Number 175493 Answers: 1 Comments: 1

tan^(−1) (asin θ)=sin^(−1) b−θ find θ.

$$\mathrm{tan}^{−\mathrm{1}} \left({a}\mathrm{sin}\:\theta\right)=\mathrm{sin}^{−\mathrm{1}} {b}−\theta \\ $$$${find}\:\theta. \\ $$

Question Number 175490 Answers: 1 Comments: 0

solve f(x)f(y)= f(x+y)+xy f:R⇒R

$${solve} \\ $$$${f}\left({x}\right){f}\left({y}\right)=\:{f}\left({x}+{y}\right)+{xy} \\ $$$${f}:\mathbb{R}\Rightarrow\mathbb{R} \\ $$

Question Number 175487 Answers: 0 Comments: 0

Question Number 175483 Answers: 2 Comments: 0

Solve it by horner′s method and get the quotient. 2x^3 y+3xy−5x^2 y^2 +12÷(2x−4)=?

$${Solve}\:{it}\:{by}\:{horner}'{s}\:{method}\:{and}\:{get} \\ $$$${the}\:{quotient}. \\ $$$$\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right)=? \\ $$

Question Number 175476 Answers: 1 Comments: 1

Question Number 175471 Answers: 1 Comments: 0

Question Number 175470 Answers: 1 Comments: 0

Question Number 175467 Answers: 0 Comments: 1

Question Number 175466 Answers: 0 Comments: 0

Question Number 175464 Answers: 2 Comments: 0

Find general solutions the following differential equations (a) (d^2 y/dx^2 ) + (dy/dx) = 6y (b) (3x^2 +y^2 )dx + (x^2 +y^2 )dy = 0

$$\:\mathrm{Find}\:\mathrm{general}\:\mathrm{solutions}\:\mathrm{the}\:\mathrm{following}\: \\ $$$$\mathrm{differential}\:\mathrm{equations} \\ $$$$\left({a}\right)\:\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:=\:\mathrm{6}{y} \\ $$$$\left(\mathrm{b}\right)\:\:\:\left(\mathrm{3}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dx}\:+\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dy}\:=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 175462 Answers: 1 Comments: 3

p^3 +q^3 +p^2 +q^2 +c^2 =0 find p+q in terms of c. if c^2 <(4/9).

$${p}^{\mathrm{3}} +{q}^{\mathrm{3}} +{p}^{\mathrm{2}} +{q}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:{p}+{q}\:{in}\:{terms}\:{of}\:{c}.\:\:{if}\:\:{c}^{\mathrm{2}} <\frac{\mathrm{4}}{\mathrm{9}}. \\ $$

Question Number 175525 Answers: 0 Comments: 0

Question Number 175521 Answers: 0 Comments: 0

Question Number 175454 Answers: 0 Comments: 0

Question Number 175452 Answers: 0 Comments: 0

Question Number 175449 Answers: 1 Comments: 1

Question Number 175450 Answers: 0 Comments: 0

Question Number 175443 Answers: 1 Comments: 0

solve for x 16^x +20^x = 25^x

$${solve}\:{for}\:{x} \\ $$$$\mathrm{16}^{{x}} +\mathrm{20}^{{x}} =\:\mathrm{25}^{{x}} \\ $$

Question Number 175436 Answers: 2 Comments: 2

∫((2x^2 +3)/( (√(3x+2))))=?

$$\int\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}}{\:\sqrt{\mathrm{3}{x}+\mathrm{2}}}=? \\ $$

Question Number 175434 Answers: 1 Comments: 0

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