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Question Number 198283    Answers: 1   Comments: 1

Given the number of consisting of 4 digits abcd such that a≤b≤c≤d is ... (A) 495 (B) 385 (C) 275 (D) 165 (E) 55

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{consisting} \\ $$$$\:\mathrm{of}\:\mathrm{4}\:\mathrm{digits}\:\mathrm{abcd}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\mathrm{a}\leqslant\mathrm{b}\leqslant\mathrm{c}\leqslant\mathrm{d}\:\mathrm{is}\:... \\ $$$$\:\left(\mathrm{A}\right)\:\mathrm{495}\:\:\:\left(\mathrm{B}\right)\:\mathrm{385}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{275} \\ $$$$\:\left(\mathrm{D}\right)\:\mathrm{165}\:\:\:\:\left(\mathrm{E}\right)\:\mathrm{55}\: \\ $$

Question Number 198282    Answers: 1   Comments: 0

Question Number 196639    Answers: 2   Comments: 0

if sinx=(2/3) then find you the value of sin^6 x+cos^6 x???

$$\mathrm{if}\:\mathrm{sinx}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{sin}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{cos}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}??? \\ $$

Question Number 196638    Answers: 0   Comments: 2

find the sum of the all 168 prime numbers from 1 to 1000. 1) 13245 2) 52788 3) 76127 4) 86344

$${find}\:{the}\:{sum}\:{of}\:{the}\:{all}\:\mathrm{168}\:{prime} \\ $$$${numbers}\:{from}\:\mathrm{1}\:{to}\:\mathrm{1000}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{13245} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{52788} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{76127} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{86344} \\ $$

Question Number 196637    Answers: 1   Comments: 0

Question Number 196635    Answers: 1   Comments: 0

Question Number 196633    Answers: 0   Comments: 1

Question Number 196628    Answers: 0   Comments: 0

inf ∅ =^? +∞ and sup ∅ =^? −∞

$${inf}\:\varnothing\:\overset{?} {=}\:+\infty\:\:\:\:{and}\:\:\:\:\:{sup}\:\varnothing\:\overset{?} {=}\:−\infty \\ $$

Question Number 196626    Answers: 0   Comments: 0

Σ_(x∈R) x = 0 and Π_(x∈R^∗ ) x = −1

$$\underset{{x}\in\mathbb{R}} {\sum}{x}\:=\:\mathrm{0}\:\:\:\:{and}\:\:\:\underset{{x}\in\mathbb{R}^{\ast} } {\prod}{x}\:=\:−\mathrm{1} \\ $$

Question Number 196625    Answers: 0   Comments: 0

Let a=BC b=CA c=AB ABC is rectangle iff tan((A^ /2))=(a/(b+c))

$${Let}\:\:{a}={BC}\:\:{b}={CA}\:\:{c}={AB} \\ $$$${ABC}\:\:{is}\:{rectangle}\:{iff}\:\:{tan}\left(\frac{\hat {{A}}}{\mathrm{2}}\right)=\frac{{a}}{{b}+{c}} \\ $$

Question Number 196788    Answers: 2   Comments: 0

calculer ∫_0 ^1 (√(1−x^2 )) <erly rolvinst>

$${calculer}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$<{erly}\:{rolvinst}> \\ $$$$ \\ $$

Question Number 196785    Answers: 1   Comments: 0

Question Number 196784    Answers: 0   Comments: 0

Question Number 196780    Answers: 0   Comments: 10

A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is?

A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is?

Question Number 196775    Answers: 0   Comments: 10

A stream is flowing at 0.75ms−¹ and a boat heading perpendicular for the stream landed at the opposite bank at an angle of 30°. Calculate the velocity of the boat. A. 1.50ms-1 B. 1.00ms-1 C. 0.86ms-1 D. 0.65ms-1

A stream is flowing at 0.75ms−¹ and a boat heading perpendicular for the stream landed at the opposite bank at an angle of 30°. Calculate the velocity of the boat. A. 1.50ms-1 B. 1.00ms-1 C. 0.86ms-1 D. 0.65ms-1

Question Number 196774    Answers: 1   Comments: 0

A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)

$$ \\ $$A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)

Question Number 196770    Answers: 1   Comments: 2

Question Number 196766    Answers: 0   Comments: 2

Question Number 196621    Answers: 1   Comments: 0

find f(x) if f(x+(√(x^2 +1))) = (x/(x+1))

$$\mathrm{find}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:\mathrm{if} \\ $$$$\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\:=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$

Question Number 196619    Answers: 1   Comments: 0

Question Number 196596    Answers: 0   Comments: 1

If f(x) = ln(((1 + x)/(1 − x))) then prove that f(((2x)/(1 + x^2 ))) = 2f(x).

$$\mathrm{If}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\frac{\mathrm{1}\:+\:{x}}{\mathrm{1}\:−\:{x}}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}\left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:=\:\mathrm{2}{f}\left({x}\right). \\ $$

Question Number 196595    Answers: 0   Comments: 0

Question Number 196594    Answers: 2   Comments: 0

Question Number 196629    Answers: 1   Comments: 1

if xyz=1, prove ((x/(x−1)))^2 +((y/(y−1)))^2 +((z/(z−1)))^2 ≥1.

$${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$

Question Number 196582    Answers: 1   Comments: 0

If x = log_a bc, y = log_b ca and z = log_c ab then prove that x + y + z = xyz − 2.

$$\mathrm{If}\:{x}\:=\:\mathrm{log}_{{a}} {bc},\:{y}\:=\:\mathrm{log}_{{b}} {ca}\:\mathrm{and}\:{z}\:=\:\mathrm{log}_{{c}} {ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{x}\:+\:{y}\:+\:{z}\:=\:{xyz}\:−\:\mathrm{2}. \\ $$

Question Number 197585    Answers: 4   Comments: 0

f (x)=f((1/x)) ⇒ f(x)=?

$$\mathrm{f}\: \left(\mathrm{x}\right)=\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

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