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Mathematics: Post your doubts here!
y =(2x-3)^3-6x dy/dx = 3(2x-3)^(2) (2) - 6 dy/dx= 6(2x-3)^(2) - 6 - dy/dx= 6(2x-3)^(2) - 6 d^2y/dx^2 = 6(2)(2x-3) d^2y/dx^2 = 48x - 72 - y=(2x^3+5x)/3x y = (2x^3)/3x + 5x/3x y = (2x^2)/3 + 5/3 Integrate with respect to 'x'. y = (2x^2)/3 + 5/3 y = (2x^3)/9 + 5x/3 Put the limits... -
Mathematics: Post your doubts here!
This question is about scaling of complex numbers and I don't think that its included in our syllabus. Still, this's how you'll do it: arg (1/3 - z) = pi/6 Assume that z' = 1/3 - z. z' = 1/3 - z 3z' = 1 - 3z 3z - 1 = -3z' Scaling a complex number (by a positive real number) doesn't... -
Mathematics: Post your doubts here!
I guess the method explained in that example is pretty easy as compared to the one which I've used to solve the other question and it won't take much time too. Secondly, you are correct; you can't calculate 'tan pi/2' and that's where we have to stop. If you try solving the question which was... -
Mathematics: Post your doubts here!
The speed with which 'B' hits the floor is equal to the initial velocity of 'A'. Therefore, we'll find the final velocity of 'B'. v = u + at v = 0 + (2.5)(1.6) v = 4 m/s The string will become slack when it reaches its maximum height. At the maximum height, A's final velocity will be 0 m/s... -
Mathematics: Post your doubts here!
Okay, so this's how you'll do this question. We have been told that arg(z-i)=pi/6 and arg(z-1)= pi/3. Let's assume that 'z = x + i y'. z - i z = x + i y z - i x + i y - i x + i (y - 1) The argument of 'z - i' is pi/6, therefore: tan^-1 [(y-1)/x] = pi/6 (y-1)/x = 1/(√3) (√3)y - √3 = x... -
Mathematics: Post your doubts here!
I presume there's something wrong with this question. If you try doing this question by sketching an argand diagram, there's no way you can do it because the lines won't ever meet as both the angles will be made from (1,0). I am attaching a similar question which I found in my book, you might... -
Mathematics: Post your doubts here!
Are both of these arguments 'arg(z-1)= pi/6' and 'arg(z-1)= pi/3' correct? -
Mathematics: Post your doubts here!
Please let me know the answer to this question. -
Mathematics: Post your doubts here!
Yes, its Applied Force > Frictional Force. I have written Frictional Force as 'uR'. -
Mathematics: Post your doubts here!
As the box has started to slide, the applied force must be greater than the frictional force. F>uR The Reaction Force (normal component) is: 20 - 12 sin a 20 - 7.2 12.8 F>uR 12 cos a > 12.8u 9.6 > 12.8u 3/4 > u -
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Mathematics: Post your doubts here!
The values of 'y' which you've calculated are wrong. This is how the curve should be: At x=0, y=3 At x=pi/4, y=0 At x=pi/2, y=-3 At x=3pi/4, y = 0 At x=pi, y=3 -
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Mathematics: Post your doubts here!
It is correct. These values are pretty much normal when finding out values in radians. -
Mathematics: Post your doubts here!
I presume you'll simply be substituting the point 'π, 0' in the equation of the normal which you've found out and show that both the sides are equal. The equation of the normal to the curve is y + x = π. Now if you substitute the point (π, 0) in this equation, the final answer is 'π = π'. -
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Mathematics: Post your doubts here!
The formula used to find the distance is indeed from O Levels. -
Mathematics: Post your doubts here!
From 3x + 4y = 0, the direction vector is (3)(4). -
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Mathematics: Post your doubts here!
This is how we'll do this question. 3x + 4y = 0 First of all, we'll be needing to find a set of coordinates on this line. We can find them by a fairly easy method. 3x + 4y = 0 4y = -3x y = -3x/4 Keep 'x=4' in the above equation so that we get 'y=-3'. Now if we put these points back...