Related questions with answers

A transducer is modeled with a current source Is and a parallel resistance $R_{s}$ . The current at the terminals of the source is measured to be 9.975 mA when an ammeter with an internal resistance of $20 \mathrm{~\Omega}$ is used. (a) If adding a $2 \mathrm{~k \Omega}$ resistor across the source terminals causes the ammeter reading to fall to 9.876 mA, calculate Is and $R_{s}$ . (b) What will the ammeter reading be if the resistance between the source terminals is changed to $4 \mathrm{~k \Omega}$ ?

Plot a line graph using this data table from a summer science camp. Determine if the graph is linear or nonlinear and label any outliers.

Year	Number of Campers
1	52
2	60
3	63
4	41
5	70

A computer scientist determines that the time in seconds it takes a particular computer to calculate n digits of $\pi$ is given by the polynomial

4.3 \times 10^{-6} n^2-2.1 \times 10^{-4} n

where 1000 $\leq$ n $\leq$ 10,000. Estimate the time it takes the computer to calculate $\pi$ to 1000 digits.

Question

A system of differential equations is given. Obtain an expression for each equilibrium (it may be a function of the constant a). $x^{\prime}=a(x-3), \quad y^{\prime}=5-y, \quad a \neq 0$

Solution

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Step 1

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Equilibria are pairs of values $(\hat{x},\hat{y})$ that simultaneously satisfy the pair of equations.

a ( \hat{x} - 3 )=0 \text{ \ and \ } 5 - \hat{y}=0

$a \neq 0$ .

We can calculate the equilibria by solving the second equation for $\hat{y}$ , and then solving the first equation for $\hat{x}$ . There is one solution to the second equation: $\hat{y}=5$ .