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Mathematics: Post your doubts here!
You're welcome. Here's Q5: Q5(i): [√(1 + x) +√(1 − x)][√(1 + x) −√(1 − x)] (1 + x) + (1-x)(1+x) - (1-x)(1+x) - (1 - x) (1 + x) - (1 - x) 2x [√(1 + x) +√(1 − x)][√(1 + x) −√(1 − x)] = 2x [√(1 + x) +√(1 − x)] = 2x / [√(1 + x) −√(1 − x)] 1 / [√(1 + x) +√(1 − x)] 1 / { 2x / [√(1 +... -
Mathematics: Post your doubts here!
You're welcome. As far as the other question is concerned, this's how it'll be done: f : x → 3x + a ff(2)=10 y = 3x + a 3 (3x + a) + a = 10 9x + 3a + a = 10 9x + 4a = 10 9(2) + 4a = 10 a = -2 g : x → b − 2x g−1(2) = 3 y = b - 2x 2x = b - y x = (b - y)/2 g−1 = (b - x)/2 y = (b -... -
Mathematics: Post your doubts here!
Q3(i): y=6e^x - e^3x (dy/dx) = 6e^x - 3e^2x 0 = 3e^x ( 2 - e^2x ) 0 = 2 - e^2x e^2x = 2 ln e^2x = ln 2 2x = ln 2 x= 0.35 Q3(ii): (dy/dx) = 6e^x - 3e^2x (d^2y/dx^2) = 6e^x - 9e^3x Substitute the value of 'x=0/35' in the above equation which we've double differentiated. If the answer is... -
Mathematics: Post your doubts here!
You don't have to set both the equations equal to each other. You'll rearrange the equation of the line so as it'll become an expression for 'x' in terms of 'y'. 2y + x = k x = k - 2y Replace 'x' with 'x = k - 2y' in the curve equation. y^2 + 2x = 13 y^2 + 2 (k - 2y) = 13 y^2 + 2k - 4y -... -
Mathematics: Post your doubts here!
Which paper; P1 or P3? And please be a little more clear on where you are getting stuck. -
Thanks for the compliment. Its pretty old now, I should probably change it.
Thanks for the compliment. Its pretty old now, I should probably change it.- ffaadyy
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Mathematics: Post your doubts here!
Talking of Argand Diagrams, the attached file might also help in the construction of Argand Diagrams and finding the least/greatest values. -
Mathematics: Post your doubts here!
Solution: sin 2Ө (dx/dӨ) = (x+1) cos 2Ө [1/(x+1)] dx = [(cos 2Ө)/(sin 2Ө)] dӨ Integrating both the sides. [1/(x+1)] dx = [(cos 2Ө)/(sin 2Ө)] dӨ ln (x+1) = (1/2) ln (sin 2Ө) + c Put x=0 and Ө=(π/12) to find the value of the constant 'c'. ln (x+1) = (1/2) ln (sin 2Ө) + c ln 1 = (1/2) ln... -
Mathematics: Post your doubts here!
Multiply the complex number '2/(-1+ i)' by the conjugate of '-1+ i' to obtain '-1 - i'. Next, find its argument using the formula 'tan x = b/a', tan x = b/a tan x = -1/-1 x = 0.785 'Tan' is positive in the third quadrant therefore we'll add this value of 'x' to that of 'π' to obtain a final... -
Mathematics: Post your doubts here!
This is the answer to a question asked by smzimran (November 2006, P3, Q9iv). First of all, we would've already constructed a circle of radius '1 unit' with centre at (1,1) as we were told to do so in the third part of this question. Coming back to the fourth part, we have to find the least... -
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Mathematics: Post your doubts here!
R=√10 a= 71.56 (√10) cos (2x - 71.57) = 2 The range in which we've to find the angle is 0<Θ<90 but we'll be needing to modify it. 0<Θ<90 multiply it by '2'. 0<2Θ<180 Subtract 71.56 from both the limits. -71.56<2Θ<108.44 So according to this range, we'll be needing to find the... -
Mathematics: Post your doubts here!
The points will be different but the overall answer will be correct. (2, 0 ,-1) is just one point, it is a line so there'll be many points on it. For e.g; if you take z=0, the point you'll get is (14/5, -7/5, 0) and this is correct too. -
Mathematics: Post your doubts here!
First of all, we'll find the common perpendicular of the two planes in question. i j k 2 -1 -3 1 2 2 i ( -2 + 6 ) + j ( -3 -4 ) + k ( 4 + 1 ) 4i - 7j + 5k '4i - 7j + 5k'; This is the common perpendicular of the two planes or more precisely, the direction vector of their line of... -
Mathematics: Post your doubts here!
[(1+sin x)/cos x] + [cos x/(1+sin x)] [(1+sin x)^2 + cos^2 x]/[(cos x)(1+sin x)] [1 + 2 sin x + sin^2 x + cos^2 x]/[(cos x)(1+sin x)] Recall the identity ' sin^2 x + cos^2 x=1'. [1 + 2 sin x + 1]/[(cos x)(1+sin x)] [2 + 2 sin x]/[(cos x)(1+sin x)] [2 (1 + sin x)]/[(cos x)(1+sin x)] As '1 +... -
Mathematics: Post your doubts here!
If it's J10, P32; then Q4(ii) will be done this way. x = tan^-1 (x) + π Take the initial value as 'π' and put it in the above formula to obtain a few iterations. 1. 4.4042 2. 4.4891 3. 4.4932 4. 4.4933 5. 4.4934 6. 4.4934 The answer is '4.49' correct to two-decimal places. If it's J10... -
Mathematics: Post your doubts here!
Refer to the above diagram and solve the horizontal and the vertical components of forces. Horizontal Component: T cos θ + T sin θ = 15.5 T cos θ = 15.5 - T sin θ Vertical Component: T cos θ + 8 = T sin θ 15.5 - T sin θ + 8 = T sin θ 23,5 = 2 T sin θ 11.75 = T sin θ Therefore, T sin θ... -
Mathematics: Post your doubts here!
(1+x+2x^2)^2 Suppose 'x+2x^2' to be one term. [1 + (x+2x^2)]^2 Now expand the above equation. [1 + (x+2x^2)]^2 1 + (x+2x^2)(2) + [(x+2x^2)^2(2)(1)]/2 1 + 2x + 4x^2 + (x+2x^2)^2 1 + 2x + 4x^2 + x^2 + 4x^3 + 4x^4 1 + 2x + 5x^2 + 4x^3 + 4x^4 Therefore, the final answer is '1 + 2x + 5x^2 +... -
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Mathematics: Post your doubts here!
This is how we'll do this question: 1/(z+2-i) We are given that ' z = 2 cos θ + i ( 1 - 2 sin θ )' so we'll put in this value of 'z' in the above equation. 1/(z+2-i) 1/[2 cos θ + i ( 1 - 2 sin θ )+2-i] Arrange the real numbers and the imaginary numbers. 1/[(2 cos θ + 2) + i ( 1 - 2 sin...