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MensurationQuestion and Answers: Page 12

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Let a,b>0 and x∈]0;(π/2)[ Prove ((a/(sinx))+1)((b/(cosx))+1)≥(1+(√(2ab)))^2

$$\left.{Let}\:{a},{b}>\mathrm{0}\:\:{and}\:{x}\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\:\right. \\ $$$$\:\:{Prove}\:\:\:\left(\frac{{a}}{{sinx}}+\mathrm{1}\right)\left(\frac{{b}}{{cosx}}+\mathrm{1}\right)\geqslant\left(\mathrm{1}+\sqrt{\mathrm{2}{ab}}\right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 117825 Answers: 1 Comments: 0

Let ABC be a triangle such as 2cosA+3sinB=4 and 3cosB+2sinA=3 Prove that the angle C is right.

$${Let}\:{ABC}\:{be}\:{a}\:{triangle}\:{such}\:{as}\: \\ $$$$\:\mathrm{2}{cosA}+\mathrm{3}{sinB}=\mathrm{4}\:{and}\:\:\mathrm{3}{cosB}+\mathrm{2}{sinA}=\mathrm{3} \\ $$$${Prove}\:{that}\:{the}\:{angle}\:{C}\:{is}\:{right}. \\ $$$$\: \\ $$

Question Number 117739 Answers: 1 Comments: 0

what is the centre of the circle with radius 4(√2) that can be inscribed in the parabola y=x^2 −16x+128?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{with}\:\mathrm{radius}\:\mathrm{4}\sqrt{\mathrm{2}}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{parabola}\: \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} −\mathrm{16x}+\mathrm{128}? \\ $$

Question Number 117414 Answers: 0 Comments: 0

Question Number 114638 Answers: 1 Comments: 0

Given a = ((1^2 +2^2 +3^2 +...+16^2 −16)/(1.3+2.4+3.5+...+15.17)) c = (1−(1/2)).(1−(1/3)).(1−(1/4)).(1−(1/5)). (1+(1/5))(1+(1/4))(1+(1/3))(1+(1/2)). find a×c =

$${Given}\:{a}\:=\:\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +...+\mathrm{16}^{\mathrm{2}} −\mathrm{16}}{\mathrm{1}.\mathrm{3}+\mathrm{2}.\mathrm{4}+\mathrm{3}.\mathrm{5}+...+\mathrm{15}.\mathrm{17}} \\ $$$$\:\:\:{c}\:=\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right).\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right).\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right).\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{5}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right). \\ $$$${find}\:{a}×{c}\:=\: \\ $$

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Question Number 114071 Answers: 1 Comments: 4

Find the solution set (√(x^2 −4x−5)) ≥ x

$${Find}\:{the}\:{solution}\:{set}\: \\ $$$$\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}}\:\geqslant\:{x} \\ $$

Question Number 113092 Answers: 2 Comments: 0

What is the area of a tringle where the sides of triangle are 91 cm, 98 cm, and 105 cm

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tringle}\:\mathrm{where}\:\mathrm{the} \\ $$$$\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{91}\:\mathrm{cm},\:\mathrm{98}\:\mathrm{cm},\:\mathrm{and}\:\mathrm{105}\:\mathrm{cm} \\ $$

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A chord which is a perpendicular bisector of radius of length 18cm in a circle, has length.

$$\mathrm{A}\:\mathrm{chord}\:\mathrm{which}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perpendicular} \\ $$$$\mathrm{bisector}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{length}\:\mathrm{18cm}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{circle},\:\mathrm{has}\:\mathrm{length}. \\ $$$$ \\ $$

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