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Question Number 198052 Answers: 1 Comments: 0

Question Number 198018 Answers: 1 Comments: 0

Question Number 197851 Answers: 0 Comments: 0

If z_1 = (√((α−β)/2)) and z_2 = (√((α+β)/2)) . Show that ∣z_1 −z_2 ∣^2 + ∣z_1 +z_2 ∣ = 2∣z∣^2 +∣z_2 ∣^2 and deduce that ∣α+(√(α^2 −β^2 ))∣ + ∣α−(√(α^2 −β^2 ))∣ = ∣α+β∣ + ∣α−β∣ Thank you in advance

$If z_{1} = \sqrt{\frac{α - β}{2}} and z_{2} = \sqrt{\frac{α + β}{2}} . Show$ $that ∣ z_{1} - z_{2} ∣^{2} + ∣ z_{1} + z_{2} ∣ = 2 ∣ z ∣^{2} + ∣ z_{2} ∣^{2} and$ $deduce that$ $∣ α + \sqrt{α^{2} - β^{2}} ∣ + ∣ α - \sqrt{α^{2} - β^{2}} ∣ = ∣ α + β ∣ + ∣ α - β ∣$ $Thank you in advance$

Question Number 197792 Answers: 2 Comments: 0

Solve the following differential equation 1) y′′ + y = e^x + x^3 , y(0)=2, y′(0)=0 2) y′′ + y^′ − 2y = x + sin2x, y(0)=1, y′(0)=0 3) y′′ − y′ = xe^x , y(0)=2, y′(0)= 1 Thank you

$Solve the following differential equation$ $1) y^{″} + y = e^{x} + x^{3}, y (0) = 2, y^{'} (0) = 0$ $2) y^{″} + y^{^{'}} - 2 y = x + \sin 2 x, y (0) = 1, y^{'} (0) = 0$ $3) y^{″} - y^{'} = {xe}^{x}, y (0) = 2, y^{'} (0) = 1$ $Thank you$

Question Number 197776 Answers: 1 Comments: 3

Question Number 197640 Answers: 1 Comments: 0

Water is leaking from a hemispheric bowl of radius 20cm at the rate of 0.5cm^3 /s. Find the rate at which surface area of the water decreasing when the water level is halfway from the top. Thank you

$W a t e r i s l e a k i n g f r o m a h e m i s p h e r i c$ $b o w l o f r a d i u s 20 c m a t t h e r a t e o f$ $0.5 {c m}^{3} / s . F i n d t h e r a t e a t w h i c h s u r f a c e$ $a r e a o f t h e w a t e r d e c r e a s i n g w h e n t h e$ $w a t e r l e v e l i s h a l f w a y f r o m t h e t o p .$ $T h a n k y o u$

Question Number 197470 Answers: 2 Comments: 0

Solve the following equation x + 2y + 2z = 0 2x + y − 2z =0 3x + 4y − 6z =0 3x − 11y + 12z = 0

$S o l v e t h e f o l l o w i n g e q u a t i o n$ $x + 2 y + 2 z = 0$ $2 x + y - 2 z = 0$ $3 x + 4 y - 6 z = 0$ $3 x - 11 y + 12 z = 0$

Question Number 197459 Answers: 0 Comments: 1

Is complex infinity big? ∞^∼ =∞∙(1+i) Their absolute value is big ∣∞^∼ ∣>∣∞∣

$Is complex infinity big ?$ $\tilde{\infty} = \infty \cdot (1 + i)$ $Their absolute value is big$ $∣ \tilde{\infty} ∣>∣ \infty ∣$

Question Number 197371 Answers: 1 Comments: 0

Question Number 197184 Answers: 1 Comments: 0

Show that log(−logi)=log((π/2))−i(π/2)

$Show that \log (- \log i) = \log (\frac{π}{2}) - i \frac{π}{2}$

Question Number 197185 Answers: 1 Comments: 0

Simplify (((((√2))^(√3) ∙((√3))^(√2) +((√2))^(√(12)) )/(((√6))^(√2) +((√2))^((√3)+(√2)) )))^(1/((√3)−(√2)))

$Simplify$ $\sqrt[\sqrt{3} - \sqrt{2}]{\frac{{(\sqrt{2})}^{\sqrt{3}} \cdot {(\sqrt{3})}^{\sqrt{2}} + {(\sqrt{2})}^{\sqrt{12}}}{{(\sqrt{6})}^{\sqrt{2}} + {(\sqrt{2})}^{\sqrt{3} + \sqrt{2}}}}$

Question Number 197089 Answers: 2 Comments: 0

Simplify (((1+(√3)i)/(1−(√3)i)))^(10)

$Simplify {(\frac{1 + \sqrt{3} i}{1 - \sqrt{3} i})}^{10}$

Question Number 197052 Answers: 1 Comments: 0

Find all the values of sin^(−1) (√2)

$Find all the values of \sin^{- 1} \sqrt{2}$

Question Number 196738 Answers: 0 Comments: 13

Question Number 196657 Answers: 0 Comments: 0

A pilot flies his plane directly from a point A to a point B, a distance of 450Km. The bearing of B from A is 030°. A wind of 80Km/hr is blowing from the east. Given that the plane can travel at 320Km/hr in still air. Find (i) The bearing on which the plane must be steered. (ii) The time taken to fly from A to B.

$A pilot flies his plane directly from a point A to a point B,$ $a distance of 450 Km . The bearing of B from A is 030 ° . A$ $wind of 80 Km / hr is blowing from the east . Given that the$ $plane can travel at 320 Km / hr in still air . Find$ $(i) The bearing on which the plane must be steered .$ $(ii) The time taken to fly from A to B .$

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?

Question Number 196567 Answers: 0 Comments: 3

Show that (((1+ itanθ)/(1− itanθ)))^n =((1+ itan(nθ))/(1− tan(nθ)))

$Show that {(\frac{1 + itan θ}{1 - itan θ})}^{n} = \frac{1 + itan (n θ)}{1 - \tan (n θ)}$

Question Number 196560 Answers: 2 Comments: 1

Question Number 196525 Answers: 1 Comments: 0

Question Number 196444 Answers: 0 Comments: 1

Question Number 196242 Answers: 2 Comments: 0

Simplify (((1+cos2θ +isin2θ)/(1+cos2θ −isin2θ)))^(30)

$Simplify {(\frac{1 + \cos 2 θ + isin 2 θ}{1 + \cos 2 θ - isin 2 θ})}^{30}$

Question Number 196211 Answers: 1 Comments: 0

Show that cos((π/3)+i)=(1/4)(e+(1/e)) −((√3)/4)(e−(1/e))i

$Show that \cos (\frac{π}{3} + i) = \frac{1}{4} (e + \frac{1}{e}) - \frac{\sqrt{3}}{4} (e - \frac{1}{e}) i$

Question Number 196205 Answers: 1 Comments: 0

What′s the value for !7 ?

${What}^{'} s the value for! 7 ?$

Question Number 195948 Answers: 0 Comments: 0

An object is said to cross a thousand kilimeters in planks constant. How many times faster is the object to the speed of light. plank′s time = 10^(−44) sec.

$An object is said to cross a thousand$ $kilimeters in planks constant . How many$ $times faster is the object to the speed of$ $light . {plank}^{'} s time = 10^{- 44} \sec .$

Question Number 195848 Answers: 2 Comments: 0

Please how did ∣z−a∣=r became z= a + re^(iθ) ?

$Please how did ∣ z - a ∣= r became$ $z = a + {re}^{i θ} ?$

Question Number 195747 Answers: 0 Comments: 3

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