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Mr Bonsu an engineer walked round a cylindrical container 4m high once keeping a constant distance of 1m from the container. If he walked with a speed of 3kmh^(−1) for three minutes, calculate to the nearest whole number the: (i) radius of the circle (ii) volume of the container

$$\mathrm{Mr}\:\mathrm{Bonsu}\:\mathrm{an}\:\mathrm{engineer}\:\mathrm{walked}\:\mathrm{round} \\ $$$$\mathrm{a}\:\mathrm{cylindrical}\:\mathrm{container}\:\mathrm{4m}\:\mathrm{high}\:\mathrm{once} \\ $$$$\mathrm{keeping}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{1m}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{container}.\:\mathrm{If}\:\mathrm{he}\:\mathrm{walked}\:\mathrm{with}\:\mathrm{a}\: \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{3kmh}^{−\mathrm{1}} \:\mathrm{for}\:\mathrm{three}\:\mathrm{minutes},\: \\ $$$$\mathrm{calculate}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number} \\ $$$$\mathrm{the}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{container} \\ $$

Question Number 152063 Answers: 2 Comments: 0

If x is a real number and y is equal to ((x^2 + 1)/(x^2 + x + 1)), show that ∣y − (4/3)∣ ≤ (2/3)

$$\mathrm{If}\:\:\mathrm{x}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:\mathrm{and}\:\:\:\mathrm{y}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:+\:\:\mathrm{1}}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mid\mathrm{y}\:\:\:−\:\:\:\frac{\mathrm{4}}{\mathrm{3}}\mid\:\:\:\leqslant\:\:\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 152061 Answers: 1 Comments: 0

solve Ω= ∫_0 ^( ∞) (( sin^( 3) (x).cos^( 2) (x))/x^( 3) )dx=^? ((7π)/(32))...■

$$ \\ $$$$\:\:\:{solve} \\ $$$$\:\:\:\: \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{3}} \left({x}\right).{cos}^{\:\mathrm{2}} \left({x}\right)}{{x}^{\:\mathrm{3}} }{dx}\overset{?} {=}\frac{\mathrm{7}\pi}{\mathrm{32}}...\blacksquare \\ $$

Question Number 152052 Answers: 1 Comments: 0

knowns x_2 =(2/x_1 ) , x_3 =(3/x_2 ) , x_4 =(4/x_3 ) , x_5 =(5/x_4 ) , ..., x_8 =(8/x_7 ). Find the value of x_1 ×x_2 ×x_3 ×...×x_8 .

$$\:\:\mathrm{knowns}\:\mathrm{x}_{\mathrm{2}} =\frac{\mathrm{2}}{\mathrm{x}_{\mathrm{1}} }\:,\:\mathrm{x}_{\mathrm{3}} =\frac{\mathrm{3}}{\mathrm{x}_{\mathrm{2}} }\:,\:\mathrm{x}_{\mathrm{4}} =\frac{\mathrm{4}}{\mathrm{x}_{\mathrm{3}} } \\ $$$$,\:\mathrm{x}_{\mathrm{5}} =\frac{\mathrm{5}}{\mathrm{x}_{\mathrm{4}} }\:,\:...,\:\mathrm{x}_{\mathrm{8}} =\frac{\mathrm{8}}{\mathrm{x}_{\mathrm{7}} }.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ×\mathrm{x}_{\mathrm{2}} ×\mathrm{x}_{\mathrm{3}} ×...×\mathrm{x}_{\mathrm{8}} . \\ $$

Question Number 152049 Answers: 0 Comments: 0

If a;b≥1 then prove that: (a+1+((a+1)/a^2 ))^a ∙ (b+1+((b+1)/b^2 ))^b ≥ 2^(2(1+(√(ab))))