Topquark

Let's say the rectangle is x by y A = xy =(x-1)(y+1) = (x+8)(y-4) which give x=10 & y=9 and so its area 90 sq cm.

Let O1 & O2 be the centres of the two circles. From P draw a tangent PT meeting the second circle at T. Likewise RS//PT is tangent to the first circle. From rt. triangle PTO2, sin(TPO2)= TO2/PO2 = 1/3. The distance between RS & PT = PR*sin(TPO2)= 4*1/3 =...

If we have a trapezoid with parallel sides of a & b then the length of the parallel line that bisects the trapezoid is = rms(a,b)= [(a^2+b^2)/2]^(1/2) In this case the parallel lines are of lengths 3*m & 9*m and thus the length of the bisector// to the y-...

Use Kepler's Third Law which states that T^2 is proportional to R^3

Assume that there are x steps in all. Lara goes up (2x/3) steps and returns half the number of steps taken to 2x/6 or to (x/3) up from start. After this there are (2x/3) steps still to go of which she once again takes (2/3)(2x/3)=(4x/9) steps to reach a s...