Question

solve.

1. according to kirchhoffs voltage law, the current, \\(i\\), in a certain circuit is \\(6.4i + 9.2i = 50.7\\), where \\(i\\) is in amps. solve this equation for \\(i\\).
2. the voltage of \\(240\text{ v}\\) in a circuit is the square root of the product of the power of \\(3600\text{ w}\\) and the resistance, \\(r\\).

(a) write this statement as an equation.
(b) solve this equation for resistance, in ohms. round your answer to the nearest ohm.

1. the power in a certain circuit of \\(4.25\text{ w}\\) is the quotient of the square of the voltage, \\(v\\), and a resistance of \\(2850\\ \omega\\).

(a) write this statement as an equation.
(b) solve this equation for the voltage in volts. round your answer to the nearest volt.

1. the impedance of \\(10\\ \omega\\) in a certain circuit is the square root of the sum of the square of the resistance of \\(4.5\\ \omega\\) and the square of the reactance, \\(x\\), in ohms.

(a) write this statement as an equation.
(b) solve this equation for the reactance, \\(x\\), in ohms. round your answer to the nearest ohm.

1. challenge: solve \\(\frac{c + 11}{3c} = 4\\).

Explanation:

Solve Question 19

Using the Linear Equations Solving knowledge point

$$
LATEXBLOCK0
$$

Solve Question 20

Using the Translating Word Problems and Algebraic Modeling knowledge points
(a) The voltage \(240\text{ V}\) is equal to the square root of the product of the power \(3600\text{ W}\) and the resistance \(R\):

$$ 240 = \sqrt{3600R} $$

(b) Solve for \(R\) using the Radical Equations Solving knowledge point:

$$
LATEXBLOCK1
$$

Solve Question 21

Using the Translating Word Problems and Algebraic Modeling knowledge points
(a) The power \(4.25\text{ W}\) is the quotient of the square of the voltage \(V^2\) and the resistance \(2850\ \Omega\):

$$ 4.25 = \frac{V^2}{2850} $$

(b) Solve for \(V\) using the Radical Equations Solving knowledge point:

$$
LATEXBLOCK2
$$

Rounding to the nearest volt gives \(V \approx 110\text{ V}\).

Solve Question 22

Using the Translating Squares and Sums and Algebraic Modeling knowledge points
(a) The impedance \(10\ \Omega\) is the square root of the sum of the square of the resistance \(4.5^2\) and the square of the reactance \(X^2\):

$$ 10 = \sqrt{4.5^2 + X^2} $$

(b) Solve for \(X\) using the Radical Equations Solving knowledge point:

$$
LATEXBLOCK3
$$

Rounding to the nearest ohm gives \(X \approx 9\ \Omega\).

Solve Question 23

Using the Linear Equations Solving knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question 19

\(I = 3.25\)

Question 20

(a) \(240 = \sqrt{3600R}\)
(b) \(R = 16\ \Omega\)

Question 21

(a) \(4.25 = \frac{V^2}{2850}\)
(b) \(V \approx 110\text{ V}\)

Question 22

(a) \(10 = \sqrt{4.5^2 + X^2}\)
(b) \(X \approx 9\ \Omega\)

Question 23

\(c = 1\)