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\(19700 - 19664 = 36\)... but answer key gives D (26). Let us recheck: \(9999 + 8888 = 18887\), \(18887 + 777 = 19664\), \(19700 - 19664 = 36\). Answer should be 36 (option A). Students should verify arithmetic carefully.
The peptidoglycan cell wall is specific to which type of organism?
Peptidoglycan (murein) is a unique polymer of sugars and amino acids found in bacterial cell walls. Archaea have pseudopeptidoglycan; eukaryotes lack it.
The integral $\displaystyle\int\dfrac{2x^{12}+5x^9}{(x^5+x^3+1)^3}\,dx$ equals (where $C$ is an arbitrary constant):
Divide numerator and denominator by $x^{15}$:
$\displaystyle\int\dfrac{2x^{-3}+5x^{-6}}{(1+x^{-2}+x^{-5})^3}\,dx$
Let $t=1+x^{-2}+x^{-5}$. Then $dt=(-2x^{-3}-5x^{-6})dx$, so the numerator (divided by $x^{15}$) gives $-dt$:
$=-\displaystyle\int\dfrac{dt}{t^3} \cdot \dfrac{1}{x^{15}/x^{15}}$
Wait — let me redo with $t = x^{-5}+x^{-3}+1$... Actually substituting directly: $t=1+x^{-2}+x^{-5}$, $-dt=(2x^{-3}+5x^{-6})dx$.
Integral $= -\int t^{-3}dt = \dfrac{1}{2t^2}+C = \dfrac{x^{10}}{2(x^5+x^3+1)^2}+C$
How is any premium on the issue of shares treated in the financial statements of a limited company?
Option A is correct.
Share premium is the excess above nominal value when shares are issued. It is recorded in the Share Premium Account, which is a capital reserve — it cannot be distributed as dividends.
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