Let a be the 2 × 2 matrix representing the rotation through an angle of α clockwise and let b be the 2 × 2 matrix representing the rotation through an angle of β counterclockwise, where 0 ≤ α, β ≤ 180◦ . for which values of α and β matrices a and b are similar?
40/31 or 1.9 i think
you can get there a couple of ways. one makes use of the secant rules that tell you
pq × pr = ps × pt
substituting for pr and pt, you have
pq × (pq + qr) = ps × (ps + st)
pq² + pq×qr = ps² + ps×st
substituting pq for ps everywhere, we have
pq² + pq×qr = pq² + pq×st
dividing by pq gives
pq + qr = pq + st
and subtracting pq leads us to the conclusion
qr = st
another way to look at it is to draw the chord qs. then δqps is an isosceles triangle, and the perpendicular bisector of qs bisects ∠p and also goes through the circle center. then the figure is symmetrical about that diameter secant, making qr ≅ st.
answer:s.a. = 486 in²
the formula of a volume of a cube:
a - length of edge
the formula of a surface area of a cube:
we have v = 729 ft³. substitute:
this means 10^(0.631) is 3^2, and 10^(1.771) is 3^7. square the second equation on both sides to get 10^(1.771*2)=3^14, so the answer is 1.771*2 or 3.442.