I do not seem to understand this question nor the Ms. I understand the box-whisker plot and its relationship to quartiles of which ##Q_2## is the Median.
This question is from an As level- statistics past paper question.
Just went through this...steps pretty clear. I refreshed on Riemann integrals { sum of rectangles approximate area under curves}. My question is on the highlighted part in Red. The approximation of area under curve may be smaller or larger than the actual value. Thus the inequality may be ##<##...
O level question; i used similarity would appreciate an easier approach for 2 marks.
The ms solution (approach) is not clear to me. Here it is;
My approach; using similarity
Any insight welcome its a 2 mark question- cannot seem to find easier way though i suspect reflection.
My interest is on the highlighted (In Red). Otherwise the other steps are clear.
We have on that part of the problem,
##(-p\sin t -q\cos t)-12(p\cos t -q \sin t)+36p\sin t +36q\cos t = 37 \sin t + 0 \cos t##
Ah I just realized we are solving a simultaneous equation for ##p## and ##q## ...
For part (b) i was able to use equations to determine the eigenvectors;
For example for ##λ =6##
##12x +5y -11z=0##
##8x-4z=0##
##32x+10y-26z=0## to give me the eigen vector,
##\begin{pmatrix}
1 \\
2 \\
2
\end{pmatrix}## and so on.
My question is to get matrix P does the arrangement of...
Thanks, i was confusing... the correct identity is
##\cos^{2} 2θ = \dfrac{1}{2}(1+\cos 4θ) ##
anyway i realized that I will still need it in doing my work ;
##\int_0^{\frac{π}{6}} [cos ^4θ] dθ= \int_0^{\frac{π}{6}} \left[\dfrac{1}{4} + \dfrac{\cos 2θ}{2} + \dfrac{\cos^{2} 2θ}{4}\right] dθ##...