Recent content by m00c0w

I plugged in the values and got the following... \arctan {2}\ + \arctan {3} = \arctan {-1} 2.35619... = -0.78539... However another solution to \arctan {-1} is -0.78539... + pi = 2.35619... which makes the statement hold true :confused: Am I not allowed to take anything other than the...

Ok, so I used the identity \tan(u+v) = \frac{\tan u + \tan v}{1-\tan u \tan v} but all it does is bring me to the equation \frac{x+y}{1-xy} = \frac{x+y}{1-xy}. I had tried substituting the values in before and found that the statement held true for both sets of x and y, but I assumed I must...

Show that \arctan{x} + \arctan {y} = \arctan { \frac{x+y}{1-xy} } when x = \frac{1}{2}\ and \y = \frac{1}{3} but not when x = 2\ and \y = 3 I've tried taking the tangent of both sides but I don't know what to do then when I've got \tan ( \arctan{x} + \arctan{y} ) = \frac{x+y}{1-xy} Any help...

For the curve y = (1/3)x^3, given that 24x + 3y +2 = 0 is the equation of the tangent to the curve at the point (p,q) find p and q. I rearranged to get y = -8x - 2/3 So the tangent gradient is -8 I differentiated to get x^2 - 9 Therefore x^2 - 9 = -8 and x = 1 or x = -1. From here...

I'm trying to calculate the radius of the circle x^2 - 2ax + y^2 - 2ay = 0 I completed the square and got to (x-a)^2 + (y-a)^2 = 2{a}^2 That would mean the radius is \sqrt{2{a}^2} right? Which would be \sqrt{2}\sqrt{a^2} \Rightarrow a\sqrt{2}... but my textbook quotes the answer as \sqrt{2a}...

Ok guys I managed to solve it :D I was wondering if you could me whether my method was the best to use in the situation though and whether or not there was a simpler way. Here goes: A(1,2) B(b,6) I worked out the gradient of AB to be 4/(b-1) I knew that the product of the gradient of AB and...

"Find all possible values of a and b given that y = ax + 14 is the perpendicular bisector of the line joining (1,2) to (b,6)" I'm totally stuck :confused: I've tried all the methods I could think of but they all lead to dead ends. I'm hoping someone can point me in the right direction. Many thanks.

If an atom has a ground state energy level of -10.4eV then why is the ionisation energy 10.4 x 1.6 x 10^-19J ? Wouldn't that amount of energy just cause the electron to move to the highest energy level? I would have thought that the energy required to ionise the atom would be any value greater...

Could someone please explain what s_f and s_i are?

Firstly I worked out how long it takes the police car to match the speed of the stolen car. I got an answer of 5 seconds using v = u + at. I then worked out that it traveled 100m in these 5 seconds using s = 1/2(u+v)t. I calculated how far the stolen car traveled in 8 seconds (3 seconds the...

Sorry I mistyped.. the police car accelerates uniformly at 8m/s².

Hi I'm extremely sorry if this is the wrong forum but it seemed the sensible choice. Here goes: "A stolen car, traveling at a constant speed of 40m/s, passes a police car parked in a lay-by. The police car sets off three seconds later, accelerating uniformly at m/s². How long does the police...

Thanks for the reply. Referring to No. 1 I am told that the rock travels in space. It accelerates from a velocity of 100m/s to 700m/s. This takes 120 seconds.

Hi I'm doing a practice test paper in preparation for my exam. I've calculated the acceleration of a rocket to be 5m/s². It now says that the average mass of the rocket is 1000kg and asks to calculate the force on the rocket. I assumed that the formula to use would be F=ma so I calculated the...

In triangle PMQ \vec{p} = \vec{PM} + \vec{MQ} . Also \vec{PM} = \vec{MR} as in they're the same distance. Could anyone explain how I get the answer please? As my test is now tomorrow :smile: