Recent content by franceboy

Homework Statement ABC is a triangle with I as the centre of the incircle and K as the centre of the circumcircle (I ≠ K). d(X) is the sum of the distances from a point X inside the triangle to the three sides. Verify if d(P)=d(Q) (P and Q are points inside the triangle), the lines PQ and IK...

Sorry thai i did not add a sketch but a GeoGebra sketch was not accepted as file. Joffan your sketch is correct. I used the symmetry so that I " only" need to proof BX / XC * CY / YA = 1 I determined all the angles and I found some similarities but they did not help to solve the problem. Is...

Homework Statement Consider an triangle ABC with M as the middle point of the side AB. On the straight line through AB you put the angle ∠ ACM at A and the angle ∠ MCB at B. Now you have two new lines. The new lines should be on the same side of AB as C. Proof that the intersection point of the...

Is there anyone who can help me?

Since z takes on it`s maximal value, z`(x)=0. z(x)=root((R-tan(a/2)*(tan(b/2)*x+tan(b/2)*d))2 - x2) I can solve the first equation with my calculator. Then I got the real x-value which differs from the x value of the center of mass. What is the next step?

My textbook covers only the lensmaker equation. With this equation I can calculate R1. But it does not tell us how to deal with the case of a lens between water and air. Is my solution for a) right?

Thank you. The function for the left rail is y=tan(b/2)*x+tan(b/2)*d . Then we have the equations x2+z2=r(y)2 The conclusion would be x2+z2=(R-tan(a/2)*(tan(b/2)*x+tan(b/2)*d))2 I think z can be expressed by z(x)=tan(y)*x+tan(y)*d. Back to the exercise: How I find out where the rail touches the...

Using sin a=tan a, I got xi= -f*xo/(f*nwater-xo). With this equation I could solve the tasks a) and b). However I was not able to solve c) because in a) we can say that the parallel ray crosses the axis in (f,0) but now this can not be said. I think the function g(x) has the same equation...

I was not able to find the equation for the intersection. Could you name this equation? And what should I do after solving this equation?

Thanks. Are my next attempts right? How do I solve this task?

Is y(x)=tan(b/2)*x+R ?

Okay y(x) is supposed to be y(x)=tan(b/2)*x And y(x)=ycircle Then we would have the equation: (R-tan(a/2)*tan(b/2)*x)2=x2+z2 And z= root((R-tan(a/2)*tan(b/2)*x)2-x2)

Homework Statement There is a small shiny object in a big aquarium, which is formed like a cuboid and filled with water. The plan site of a plano-convex lens with a focal length f is put on the wall of the aquarium from outside. The object is located on the optical axis of the lens. The...

Sorry for answering so late. Okay we imagine that the CM is the point CM=(xCM, 0 , R+xCM*(tan(y)-tan(b/2)*tan(a/2)). Then the varying is dependent from the value of y. We can say: r=R-tan(a/2)*ycircle The centre of the circle is (xCM , ycircle , R+xCM*(tan(y)-tan(b/2)*tan(a/2)). The circle is...

I failed at describing the double cone with vectors and finding an intersection equation. Could you help me?