The circumference of the circle after t seconds = 25.12 t
Given data,
The radius of each circular wave will increase by four centimeters per second (cm/s)
In 1 second of circular wave radius = 4cm
In 1*t second of circular wave radius = 4t cm
As a result, the radius of the circular wave after t seconds is 4t cm.
We already know that the circumference of a circle is given by = 2πr, where r is the circle's radius.
As a result, the radius of a circular wave after t seconds is = 2π * radius of a circular wave after t seconds = 2π * 4t
= 8πt
( Taking π = 3.14 )
As a result, the circumference of the circle after t seconds = 8πt
= 3.14t
= 25.12t
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A thermostat is a switch that operates itself when the temperature
goes above or below a temperature that the user can set.
-- Before you go to bed, you set the thermostat for 65° .
If the temperature in the house goes below 65° during the night,
the thermostat turns on the furnace, and keeps it running until
the house warms up to 65°. Then it shuts the furnace off.
-- After breakfast, you set the thermostat for 75°.
If the temperature in the house goes above 75°, during the day,
the thermostat turns on the air conditioner, and keeps it running until
the house cools down to 75°. Then it shuts the air conditioner off.
-- On Sunday morning, you put the slow cooker on the kitchen counter,
and you throw in a big roast, a sliced onion, some baby carrots, some
sliced potatoes, some vegetable stock, salt, pepper, garlic, chili powder,
and tomato paste. Then you put the cover on, turn the power on, and
set the slow cooker to "LOW". The heater in the slow cooker turns on.
Whenever the temperature in the crock gets higher than 160°, the
thermostat in the slow cooker turns off the heater, and keeps it off
until the crock cools down to 160°. Then the thermostat turns the
heater on again.
By dinner time, you have a hot, juicy, scrumptious pot roast, ready
to eat. It's not too hot, not too cold, not too tough, not dried out, and
it melts in your mouth.
You're still thinking about it when you go to bed, and your mom gives you
a slice to take to school for your lunch on Monday.
Answer:
the wavelength λ of the light when it is traveling in air = 560 nm
the smallest thickness t of the air film = 140 nm
Explanation:
From the question; the path difference is Δx = 2t (since the condition of the phase difference in the maxima and minima gets interchanged)
Now for constructive interference;
Δx= 
replacing ;
Δx = 2t ; we have:
2t =
Given that thickness t = 700 nm
Then
2× 700 = --- equation (1)
For thickness t = 980 nm that is next to constructive interference
2× 980 = ----- equation (2)
Equating the difference of equation (2) and equation (1); we have:'
λ = (2 × 980) - ( 2× 700 )
λ = 1960 - 1400
λ = 560 nm
Thus; the wavelength λ of the light when it is traveling in air = 560 nm
b)
For the smallest thickness 
∴ 
Thus, the smallest thickness t of the air film = 140 nm
Explanation:
Given:
x₀ = 0 m
y₀ = 0 m
v₀ = 20 m/s
θ = 35°
aᵧ = -9.8 m/s²
1) Find t when y = 0.
y = y₀ + v₀ᵧ t + ½ aᵧ t²
0 = 0 + (20 sin 35°) t + ½ (-9.8) t²
0 = t (20 sin 35° - 4.9 t)
t = 0, t = 2.34
The ball stays in the air 2.34 seconds.
2) Find y when vᵧ = 0.
vᵧ² = v₀ᵧ² + 2aᵧ (y - y₀)
0² = (20 sin 35)² + 2(-9.8) (y - 0)
y = 6.71 m
The ball reaches a maximum height of 6.71 meters.
3) Find x when y = 0.
x = x₀ + v₀ₓ t + ½ aₓ t²
x = 0 + (20 cos 35°) (2.34) + ½ (0) (2.3)²
x = 38.4 m
The ball lands 38.4 meters from Tom.
4) Find v when y = 0.
vₓ = aₓ t + v₀ₓ
vₓ = (0) (2.34) + 20 cos 35°
vₓ = 16.4 m/s
vᵧ = aᵧ t + v₀ᵧ
vᵧ = (-9.8) (2.34) + 20 sin 35°
vᵧ = -11.5 m/s
v = √(vₓ² + vᵧ²)
v = √((16.4)² + (-11.5)²)
v = 20 m/s
The ball has a speed of 20 m/s just before it lands.
Answer:
Explanation:
A ) initial velocity u = 12 m /s
final velocity v = 6 m /s
height = h
acceleration = - g = - 9.8 m /s²
v² = u² - 2gh
6² = 12² - 2 x 9.8 x h
h = 5.51 m
B )
Let the final velocity when energy becomes half be V at height H
kinetic energy at height h = 1/2 m V²
Given ,
.5 x 1 / 2 m x 12² = 1/2 m x V²
V² = 12² / 2
V = 8.486 m /s
V² = u² - 2 gH
8.486² = 12² - 2 x 9.8 x H
H = 3.67 m .
