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Question Number 80639 Answers: 0 Comments: 2

((log_2 ^2 (x−4)−log_2 (4−x)^8 +16)/(30−3x−(4−x)^2 )) ≥ 0

$$\frac{\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \:\left({x}−\mathrm{4}\right)−\mathrm{log}_{\mathrm{2}} \left(\mathrm{4}−{x}\right)^{\mathrm{8}} +\mathrm{16}}{\mathrm{30}−\mathrm{3}{x}−\left(\mathrm{4}−{x}\right)^{\mathrm{2}} }\:\geqslant\:\mathrm{0} \\ $$

Question Number 80620 Answers: 0 Comments: 1

Question Number 80614 Answers: 0 Comments: 1

Question Number 80613 Answers: 1 Comments: 2

Q.find (d/dx)(x!)

$${Q}.{find}\:\:\:\frac{{d}}{{dx}}\left({x}!\right) \\ $$

Question Number 80612 Answers: 0 Comments: 3

Ψ(x)=∫_1 ^x (1/(√(1−e^t ))) dt ∀x∈R prove that Ψ(x)=2ln(((1−(√(1−e^x )))/(1−(√(1−e)))))−x+1

$$\:\Psi\left({x}\right)=\int_{\mathrm{1}} ^{{x}} \frac{\mathrm{1}}{\sqrt{\mathrm{1}−{e}^{{t}} }}\:{dt}\:\:\:\:\:\forall{x}\in\mathbb{R} \\ $$$${prove}\:{that} \\ $$$$\Psi\left({x}\right)=\mathrm{2}{ln}\left(\frac{\mathrm{1}−\sqrt{\mathrm{1}−{e}^{{x}} }}{\mathrm{1}−\sqrt{\mathrm{1}−{e}}}\right)−{x}+\mathrm{1} \\ $$

Question Number 80607 Answers: 0 Comments: 0

Question Number 80595 Answers: 1 Comments: 2

Question Number 80587 Answers: 1 Comments: 6

Question Number 80586 Answers: 0 Comments: 1

Question Number 80585 Answers: 0 Comments: 9

Question Number 80580 Answers: 2 Comments: 0

Find general solution for k such that 7^k ≡1 mod (35)

$${Find}\:{general}\:{solution}\:{for}\:{k}\:{such}\:{that} \\ $$$$\mathrm{7}^{{k}} \equiv\mathrm{1}\:{mod}\:\left(\mathrm{35}\right) \\ $$

Question Number 80559 Answers: 0 Comments: 0

Question Number 80550 Answers: 1 Comments: 1

Question Number 80574 Answers: 1 Comments: 2

Question Number 80543 Answers: 1 Comments: 6

Question Number 80540 Answers: 0 Comments: 1

Question Number 80539 Answers: 0 Comments: 1

Question Number 80529 Answers: 0 Comments: 1

Question Number 80519 Answers: 2 Comments: 2

g(x)=2cos^2 x+sin(2x). g′(x)= ..........?

$$\mathrm{g}\left({x}\right)=\mathrm{2}{cos}^{\mathrm{2}} {x}+{sin}\left(\mathrm{2}{x}\right). \\ $$$${g}'\left({x}\right)=\:..........? \\ $$

Question Number 80515 Answers: 0 Comments: 1

∫(dx/((1+x^φ )^φ ))

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\phi} \right)^{\phi} } \\ $$

Question Number 80508 Answers: 0 Comments: 4

solve the D.E x^2 +(y^2 +1)dx+y(√(x^3 +1)) dy=0

$${solve}\:{the}\:{D}.{E}\: \\ $$$${x}^{\mathrm{2}} +\left({y}^{\mathrm{2}} +\mathrm{1}\right){dx}+{y}\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dy}=\mathrm{0} \\ $$

Question Number 80505 Answers: 0 Comments: 8

Given that 7^k ≡1 (mod 15) a) Write down three values of k. b) Find the general solution of the equation 7^k ≡ 1 (mod 15)

$$\mathrm{Given}\:\mathrm{that}\:\:\mathrm{7}^{{k}} \:\equiv\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{15}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Write}\:\mathrm{down}\:\mathrm{three}\:\mathrm{values}\:\mathrm{of}\:{k}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\:\mathrm{7}^{{k}} \:\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{15}\right) \\ $$

Question Number 80493 Answers: 0 Comments: 4

Solve for a, b and c a + b + c = (1/2) ..... (i) abc = − (1/4) ...... (iii) ab + ac + bc = (3/2) ...... (iv)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c} \\ $$$$\:\:\:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\mathrm{abc}\:\:\:=\:\:\:−\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:......\:\left(\mathrm{iii}\right) \\ $$$$\:\:\:\:\:\:\mathrm{ab}\:+\:\mathrm{ac}\:+\:\mathrm{bc}\:\:\:=\:\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\:\:......\:\left(\mathrm{iv}\right) \\ $$

Question Number 80485 Answers: 0 Comments: 1

what is the king rule?

$${what}\:{is}\:{the}\:{king}\:\:{rule}? \\ $$

Question Number 80477 Answers: 0 Comments: 5

Question Number 80475 Answers: 0 Comments: 0

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