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faust18 [17]
3 years ago
9

Y=x^2-16x+63

Formula1" title="y = x { }^{2} - 16x + 63 \\ " alt="y = x { }^{2} - 16x + 63 \\ " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Nana76 [90]3 years ago
5 0
◆ QUADRATIC EQUATIONS ◆

given \: expression \: - \\ \\ y = {x}^{2} - 16x + 63 \\ \\ y = {x}^{2} - 7x - 9x + 63 \\ \\ y = x(x - 7) - 9(x - 7) \\ \\ y = (x - 9)(x - 7) \: \: \: \: \: \: ans. \\ \\ \\ additional \: calculation \: - \\ \\ had \: been \: \: y = 0 \\ \\ we \: would \: have \: got \: \\ x = 9 \: \: \: \: \: or \: \: \: \: \: x = 7
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Answer:

\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx}= x - \ln(1 + e^{x}) + C\end{aligned}.

Step-by-step explanation:

The first derivative of the denominator 1 + e^{x} is e^{x}. Rewrite the fraction to obtain that expression on the numerator.

\begin{aligned}\frac{1}{1 + e^{x}} &= \frac{1 + e^{x}}{1 + e^{x}} - \frac{e^{x}}{1+e^{x}}\\&=1-\frac{e^{x}}{1+e^{x}}\end{aligned}.

In other words,

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