Math Is Fun Forum

Hi, I dont know how many questions im allowed to ask on here, so just tell me enough is enough when i get too carried away

These types of questions are giving me alot of grief..

1. Show that any two tangent lines to the parabola y=ax², a≠0,intersect at a point that is on the vertical line halfway between the points of tangency

2. Suppose L is the tangent line at x=x0 to the graph of the cubic equation y=ax ³ +bx. Find the x-coordinate of the point where L intersects the graph a second time.

3.Show that the segment of the tangent line to the graph of y=1/x that is cut off by the coordinate axes is bisected by the point of tangency.

Thanks for the help

A(7,2) and C(1,4) are two vertices of a square ABCD

(a) Find the equation of the diagonal BD.
(b) Find the coordinates of B and D.

I have answered (a), but i cant seem to get (b), can someone please show me how to get (b). thanks=)

find the domain of

1/(sqrtx  -2)

I think the answer is x≥0 x≠4 but book says x>2 can someone please help me out,  show me an algebraic way to solve these types of problems=) thanks

18x -24x^2=0 

Can someone please give me an explanation of how to complete these types of problems, thanks

At the Olympic Games 40 years ago, the average number of competitors per sport was 5 times the number of sports played.

In 2004 there were 10 more sports than there were 40 years ago. In 2004 the average number of competitors per sport was 3.5 times greater than 40 years ago. At the 2004 Olympic Games there were 10500 competitors.

Write at least one equation to model this situation. Use the model to find the number of sports played at the Olympic Games 40 years ago.

Hi, can anyone please give me a few practice questions similar to:

One integer is 5 more than twice another integer.
The squares of these two integers have a difference of 312.

Integers are ______ and _______

It would be really helpful if u can show full explanations aswel, thanks so much if someone could do this!!!!