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Question Number 72744 Answers: 0 Comments: 0

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Question Number 72734 Answers: 3 Comments: 0

A triangle ABC is inscribed in a circle.AC=10cm,BC=7cm and AB=10cm.Find the radius of the circle.

$${A}\:{triangle}\:{ABC}\:{is}\:{inscribed}\:{in}\:{a} \\ $$$${circle}.{AC}=\mathrm{10}{cm},{BC}=\mathrm{7}{cm}\:{and}\: \\ $$$${AB}=\mathrm{10}{cm}.{Find}\:{the}\:{radius}\:{of}\:{the} \\ $$$${circle}. \\ $$

Question Number 72724 Answers: 0 Comments: 2

Question Number 72721 Answers: 1 Comments: 12

Question Number 72718 Answers: 0 Comments: 3

given that a ≡ b(mod n) show that a^k ≡ b^k (mod n)

$${given}\:{that}\: \\ $$$$\:{a}\:\equiv\:{b}\left({mod}\:{n}\right)\: \\ $$$${show}\:{that}\:{a}^{{k}} \:\equiv\:{b}^{{k}} \:\left({mod}\:{n}\right) \\ $$

Question Number 72689 Answers: 1 Comments: 0

Question Number 72688 Answers: 3 Comments: 0

Evaluate lim_(t→9) ((9−t)/(3−(√t) ))

$${Evaluate}\: \\ $$$$\:\underset{{t}\rightarrow\mathrm{9}} {\:{lim}}\frac{\mathrm{9}−{t}}{\mathrm{3}−\sqrt{{t}}\:} \\ $$

Question Number 72672 Answers: 2 Comments: 2

Question Number 72671 Answers: 0 Comments: 1

Question Number 72694 Answers: 0 Comments: 3

convergent or divergent? S=(2/1)−(1/1)+(2/3)−(1/3)+(2/5)−(1/5)+(2/7)−(1/7)...

$$\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}? \\ $$$${S}=\frac{\mathrm{2}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{2}}{\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{7}}... \\ $$

Question Number 72693 Answers: 1 Comments: 0

prove that the arithmetic mean of a sequence is greater or equal to the geometric mean. that is ((a + b)/2) ≥ (√(ab))

$${prove}\:{that}\:{the}\:{arithmetic}\:{mean}\:{of}\:{a}\:{sequence} \\ $$$${is}\:{greater}\:{or}\:{equal}\:{to}\:{the}\:{geometric}\:{mean}. \\ $$$${that}\:\:{is}\:\: \\ $$$$\:\:\:\:\frac{{a}\:+\:{b}}{\mathrm{2}}\:\geqslant\:\sqrt{{ab}}\: \\ $$

Question Number 72668 Answers: 1 Comments: 0

Question Number 72665 Answers: 1 Comments: 5

∫_( 2) ^( 3) ((tan^(−1) (x))/(1 − x^2 )) dx

$$\int_{\:\mathrm{2}} ^{\:\mathrm{3}} \:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 72641 Answers: 0 Comments: 2

Question Number 72640 Answers: 3 Comments: 0

Question Number 72639 Answers: 1 Comments: 0

prove:(π/5)(3^2 +4^2 )^(1/2) =π

$${prove}:\frac{\pi}{\mathrm{5}}\left(\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\pi \\ $$

Question Number 72634 Answers: 1 Comments: 4

help me with the conditions please for a function f to be continuous at a point a

$${help}\:{me}\:{with}\:{the}\:{conditions}\:{please}\: \\ $$$${for}\:{a}\:{function}\:{f}\:{to}\:{be}\:{continuous}\:{at}\:{a}\:{point}\:{a} \\ $$

Question Number 72633 Answers: 0 Comments: 0

prove using th sandwich or Squeez theorem that for any a > 0 lim_(x→a) (√x) = (√a)

$${prove}\:{using}\:{th}\:{sandwich}\:{or}\:{Squeez}\:{theorem}\:{that} \\ $$$${for}\:{any}\:\:{a}\:>\:\mathrm{0} \\ $$$$\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$

Question Number 72666 Answers: 1 Comments: 0

Question Number 72628 Answers: 0 Comments: 2

solve the inequality log_3 (2x^2 + 9x + 9) < 0

$${solve}\:{the}\:{inequality}\: \\ $$$$\:\:{log}_{\mathrm{3}} \left(\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:+\:\mathrm{9}\right)\:<\:\mathrm{0} \\ $$

Question Number 72608 Answers: 1 Comments: 0

Question Number 72606 Answers: 2 Comments: 0

Question Number 72603 Answers: 1 Comments: 0

Question Number 72595 Answers: 1 Comments: 3

(α+β)^2 = α^2 + 2αβ + β^(2 )

$$\left(\alpha+\beta\right)^{\mathrm{2}} \:=\:\alpha^{\mathrm{2}} \:+\:\mathrm{2}\alpha\beta\:+\:\beta^{\mathrm{2}\:} \\ $$

Question Number 72593 Answers: 2 Comments: 0

If the length of a square is increased by 25% while its width is decrease by 15% to form a rectangle. What is the ratio of the area of the rectangle to the area of the square

$$\mathrm{If}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:\:\mathrm{25\%}\:\mathrm{while}\:\mathrm{its} \\ $$$$\mathrm{width}\:\mathrm{is}\:\mathrm{decrease}\:\mathrm{by}\:\:\:\mathrm{15\%}\:\:\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{rectangle}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square} \\ $$

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