Answer:
The output power of the circuit is 3 Watts.
Given:
a loss in decibels = 3 dB
Input power = 6 Watts
To find:
What is the output power?
Formula used:
Output power = Input power × loss in ratio
Solution:
3 dB loss corresponds to a ratio of 0.5
Output power can be calculated as follows:
Output power = Input power × loss in ratio
Output power = 6 × 0.5
Output power = 3 Watts
Therefore, the output power of the circuit is 3 Watts.
Answer:
The rate at which the root beer level is decreasing is 0.08603 cm/s.
Explanation:
The formula for the volume of the cone is:
Where V denotes the cone's volume
r indicates the radius
h signifies the height
The ratio of radius to height remains consistent throughout the cone.
Thus, we have r = d / 2 = 10 / 2 cm = 5 cm
h is 13 cm
Consequently, r / h = 5 / 13
r = {5 / 13} h
Additionally, we differentiate the volume expression in relation to time:
Given that 
= -4 cm³/sec (the negative sign indicates outflow)
h equals 10 cm
Hence,
The rate at which the root beer level is decreasing is 0.08603 cm/s.
Answer:
The rotational angular speed is measured at 1.34 rad/s.
Explanation:
Considering the following parameters,
Length = 3.40 m
Distance = 5.90 m
Angle = 45.0°
We are tasked with finding the angular speed of rotation
Using the balance equation
Horizontal component
Vertical component
Substituting the tension value
Substituting the value into the equation
Thus, the angular speed of rotation computes to 1.34 rad/s.
Δd = 23 cm. When the eta string of the guitar has nodes at both ends, the resulting waves create a standing wave, which can be expressed with the following formulas: Fundamental: L = ½ λ, 1st harmonic: L = 2 ( λ / 2), 2nd harmonic: L = 3 ( λ / 2), Harmonic n: L = n λ / 2, where n is an integer. The rope's speed can be calculated using the formula v = λ f. This speed remains constant based on the tension and linear density of the rope. Now, let's determine the speed with the provided data: v = 0.69 × 196, yielding v = 135.24 m/s. Next, we will find the wavelengths for the two frequencies: λ₁ = v / f₁, which gives λ₁ = 135.24 / 233.08, equaling λ₁ = 0.58022 m; λ₂ = v / f₂ results in λ₂ = 135.24 / 246.94, consequently λ₂ = 0.54766 m. We'll substitute into the resonance equation Lₙ = n λ/2. At the third fret, m = 3, therefore L₃ = 3 × 0.58022 / 2, resulting in L₃ = 0.87033 m. For the fourth fret, m = 4, which gives L₄ = 4 × 0.54766 / 2, equating to L₄ = 1.09532 m. The distance between the two frets is Δd = L₄ – L₃, so Δd = 1.09532 - 0.87033, leading to Δd = 0.22499 m or 22.5 cm, rounded to 23 cm.
a) 0.13*τ; b) 2.08*τ. To describe the discharging process of a capacitor through a resistor, consider the following: Q(t) = Qo * exp(-t/τ) to signify a loss of 1/8 of its charge. In this scenario, Q(t) = 7/8 * Qo = 7/8 * exp(-t/τ). By rearranging, we have ln(7/8)*τ = -t, thus t = -ln(7/8)*τ = 0.13. For a loss of 7/8 of its charge, we use Q(t) = 1/7 * Qo * exp(-t/τ), leading to t = -ln(1/8)*τ = 2.08.
