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Mathematics: Post your doubts here!
dy/dx = y(4-y) [1/y(4-y)].dy = 1.dx As we can't directly integrate [1/y(4-y)], we'll use its partial fractions form which we've found out in part (i) of this question. [1/y(4-y)] dy = 1 dx Replace '[1/y(4-y)]' with '(1/4)(1/y) - (1/4)[1/(4-y)] ' (1/4)(1/y) - (1/4)[1/(4-y)] dy = 1 dx... -
Mathematics: Post your doubts here!
We know that the length of the wire equals to 80cm therefore the sum of the perimeter of the square and the perimeter of the circle should be equal to 80cm. 4x + 2πr = 80 2x + πr = 40 r = (40 - 2x)/π Next, we are told that the total area of the circle and that of the square is equal to A... -
Mathematics: Post your doubts here!
If the base of the Log is same (5 in this case) and that when there is a negative sign between two log function's, they are divided. Just like this: log5(4-x) - log5(x^2) = 1 log5[(4-x)/(x^2)] = 1 And once we've a function in this form 'logA(B) = C', we can write it as 'B = A^C'. This is why... -
Mathematics: Post your doubts here!
log5(4-x) - 2log5(x) = 1 log5(4-x) - log5(x)^2 = 1 log5[(4-x)/(x^2)] = 1 (4-x)/(x^2) = 5 5x^2 + x - 4 = 0 5x^2 + 5x - 4x - 4 = 0 (5x - 4) (x + 1) = 0 Keeping in mind the limit 0<x<4, the answer is '4/5'. -
Mathematics: Post your doubts here!
Q10(i) r = i −2k +s(2i +j +3k) x(L) = 1 + 2s y(L) = s z(L) = -2 + 3s r = 6i −5j +4k +t(i −2j +k) x(M) = 6 + t y(M) = -5 - 2t z(M) = 4 + t Equate x(L) with x(M). 1 + 2s = 6 + t -5 + 2s = t Equate y(L) with y(M). s = -5 - 2t s = -5 - 2(-5 + 2s) 5s = 5 s=1 Substitute s=1 in '-5 +... -
Mathematics: Post your doubts here!
Q4. We'll be needing to separately differentiate both 'x' and 'y'. √x +√y = √a Differentiating 'x' and 'y': (-1/2√x) + (-1/2√y)(dy/dx) = 0 -1/2√x = (1/2√y)(dy/dx) We'll now take the term in 'y' on the other side so as the equation will be dy/dx in terms of 'x' and 'y'. -(2√y)/(2√x) =... -
Mathematics: Post your doubts here!
When you'll integrate '1/(10-a)', the integrand will come out to be '-ln (10-a)'. -
Mathematics: Post your doubts here!
June 2007, Q9(ii): In this part, we need to find the acute angle between the plane ABC and the plane OAB. We'll be needing the common perpendiculars of both of these planes and then using the formula "(common perpendicular of ABC) x (common perpendicular of OAB) = (modulus of the common... -
Mathematics: Post your doubts here!
November 2006, Q9(iv): First of all, we'll sketch an argand diagram showing the point representing the complex number 'u' which's '1 + i'. Next, we'll draw a circle of radius '1'' with its centre at '1 + i'. Now to calculate the least value of |z|, you'll be needing to take a look at this... -
Mathematics: Post your doubts here!
The triangle ABC consists of the sides AB, AC and BC. We know that AC = 16cm and that θ = 1/3π. therefore, using these details, we'll calculate the length of sides AB and BC & then the perimeter of the triangle. To find the length of AB, we'll use the cosine rule. AB^2 = OA^2 + OB^2 - 2 (OA)... -
Mathematics: Post your doubts here!
In this question, we'll be needing to take the substitution 'x = 1 - u' but then again such questions don't come in the A Level P3's in which we have to assume a substitution ourselves. Still I 'll do it for you, here's how its done: (x^2) * [( 1 - x )^1/2] dx Take the substitution 'x = 1 -... -
Mathematics: Post your doubts here!
y = e^x - 8e^-2x y = 0 0 = e^x - 8e^-2x 8e^-2x = e^x 8 = (e^x)/(e^-2x) 8 = e^3x ln 8 = ln e^3x ln 8 = 3x 0.69 = x -
Mathematics: Post your doubts here!
In the second part of the question, we have calculated the height at which the particles are and the speed with which they've moved as soon as the string is cut. Using these details and the fact that both the particles are moving vertically under gravity, we'll find the time taken for each of... -
Mathematics: Post your doubts here!
What's the answer to this question? -
Mathematics: Post your doubts here!
In the first part, you'll obtain the answer '64 - 192x + 240x^2'. For the second part, you'll multiply '64 - 192x + 240x^2' with '1 + kx' and equate the coefficients of 'x^2' to 0. Like this: (1 + kx) (64 - 192x + 240x^2) 64 - 192x + 240x^2 + 64kx - 192kx^2 + 240kx^3 Take the coefficients of... -
Mathematics: Post your doubts here!
Wrong solution to this question, we'll use 3^y=2/3. -
Mathematics: Post your doubts here!
If we compare the equation 'f(x) = 12x^3 + 25x^2 − 4x − 12' with the equation '12 × 27^y + 25 × 9^y − 4 × 3^y − 12', it is seen that 'x' has been replaced with '3^y' in the second equation; therefore, we assume that 'x=3^y'. Now to find the value of 'y', we'll use the equation 'x=3^y' with '2/3'... -
Mathematics: Post your doubts here!
The final answer isn't correct. This's how this question will be done: sin 2Ө dx = (x + 1) cos 2Ө dӨ (dx)/(x+1) = [(cos 2Ө) / (sin 2Ө)] dӨ ln (x + 1) = (1/2) ln (sin 2Ө) + k Now to find the value of the constant 'k', we'll substitute 'Ө' with 'pie/12' and 'x' with '0'. 0 = (1/2) ln (1/2)... -
Mathematics: Post your doubts here!
Somebody had asked the same question few pages back, this's how it'll be done. -
Mathematics: Post your doubts here!
We have to 'find the coordinates of the point of intersection of the tangents to the graph y=x^2 at the points at which it meets the line with equation y=x+2'. In simple words, the points at which the graph 'y=x^2' meets the line 'y=x+2', we have to find the 2 tangent equations at those points...