In each of the Problems below, determine the critical point x = x⁰, and then classify its type and examine its stability by making the transformation x = x⁰ + u.

1. dx/ dt = [ 1 1 [ 2
x −
1 −1 ] 0 ]

2. dx/ dt = [ -2 1 [ -2
x −
1 −2 ] 1 ]

3. dx/ dt = [ -1 -1 [ -1
x −
2 −1 ] 5 ]

4. dx/ dt = [ 0 −β [ α
x − α, β, γ, δ > 0
δ 0 ] −γ ]

\bf xy=1\iff y = \cfrac{1}{x}\iff y = x^{-1}

\cfrac{dy}{dt}=-x^{-2}\cdot \cfrac{dx}{dt}\impliedby \textit{using the chain-rule}

\left. \cfrac{dy}{dt}=-\cfrac{\frac{dx}{dt}}{x^2} \right|{
\begin{array}{}
x=2\\
\frac{dx}{dt}=-2
\end{array}}\implies \cfrac{dy}{dt}=-\cfrac{-2}{2^2}

Step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%