View attachment 31910
In the diagram, there are 3 circles which are all externally tangent to each other and a semi circle. The shaded area is equal to 120. find the unshaded area of the semi circle
yes of course, because the semicircle and the smaller circle are also tangent(internally), the centres and the point of contact are colinear. isn't this a theorem in circle geometry?the line from the center of the semi circle to the point where one of the small circles are tangent to the cyrved bit of the semi circle also goes rhrough the center of the small circle?
b^2 = a^2 (e^2-1),Simple question:
LOL. I lose a markb^2 = a^2 (e^2-1),
e^2 = a^2+b^2/a^2
e = 17/15
Suppose , where a and b are coprime positive integers.
Why did you need the 'coprime' ?Suppose , where a and b are coprime positive integers.
Then .
This is a contradiction because the LHS ends in 0 in base 10, whereas the RHS cannot end in 0 (the last digits of powers of 8 go in the repeating cycle 8,4,2,6,8,4,2,6,8,....).
bl. I'm assuming you used a^2-b^2/a^2 ? (for ellipse)LOL. I lose a mark
I didn't for this proof, but I'm used to writing a rational number as a fraction in its lowest terms, so I wrote coprime without thinking too much about it.Why did you need the 'coprime' ?
adding up all five equations we obtain or then subtracting this equation from each of the original equations respectively
when the speed is q, no side force, we have which yields ....(1)A car takes a banked curve of a racing track at p m/s, the lateral gradient angle being designed to reduce the tendency to side-slip to zero for a lower speed q.
Show that the coefficient of friction necessary to prevent side-slip for the greater speed p must be at least:
Loved it!next question