Answer:
C- Choosing variables and controls
Explanation:
Correct on edge.
Answer:
(a) Wavelength is 0.436 m
(b) Length is 0.872 m
(c) 11.518 m/s
Solution:
As per the question:
The eqn of the displacement is given by:
![y(x, t) = (1.22 cm)sin[14.4 m^{- 1}x]cos[(166\ rad/s)t]](https://tex.z-dn.net/?f=y%28x%2C%20t%29%20%3D%20%281.22%20cm%29sin%5B14.4%20m%5E%7B-%201%7Dx%5Dcos%5B%28166%5C%20rad%2Fs%29t%5D)
(1)
n = 4
Now,
We know the standard eqn is given by:
(2)
Now, on comparing eqn (1) and (2):
A = 1.22 cm
K = 
where
A = Amplitude
K = Propagation constant
= angular velocity
Now, to calculate the string's wavelength,
(a) 
where
K = propagation vector
(b) The length of the string is given by:
(c) Now, we first find the frequency of the wave:
Now,
Speed of the wave is given by:
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Answer:
b -algae
Explanation:
The most common producers in aquatic ecosystems are the algae. They are called phytoplanktons.
- In the food web and food chain of aquatic ecosystems, they usually set out with the algae.
- These algae are called phytoplanktons.
- They are the producers in all aquatic ecosystem.
- Phytoplanktons consists of algae and cyanobacteria.
- Just like plants on land, phytoplanktons manufacture food in an aquatic ecosystem.
The volume of the balloon is given by:
V = 4πr³/3
V = volume, r = radius
Differentiate both sides with respect to time t:
dV/dt = 4πr²(dr/dt)
Isolate dr/dt:
dr/dt = (dV/dt)/(4πr²)
Given values:
dV/dt = 72ft³/min
r = 3ft
Plug in and solve for dr/dt:
dr/dt = 72/(4π(3)²)
dr/dt = 0.64ft/min
The radius is increasing at a rate of 0.64ft/min
The surface area of the balloon is given by:
A = 4πr²
A = surface area, r = radius
Differentiate both sides with respect to time t:
dA/dt = 8πr(dr/dt)
Given values:
r = 3ft
dr/dt = 0.64ft/min
Plug in and solve for dA/dt:
dA/dt = 8π(3)(0.64)
dA/dt = 48.25ft²/min
The surface area is changing at a rate of 48.25ft²/min
