Answer:
-13.18°C
Explanation:
To develop the problem it is necessary to consider the concepts related to the thermal conduction rate.
Its definition is given by the function
Where,
Q = The amount of heat transferred
t = time
k = Thermal conductivity constant
A = Cross-sectional area
The difference in temperature between one side of the material and the other
d= thickness of the material
The problem says that there is a loss of heat twice that of the initial state, that is
Replacing,
Solvinf for 
,
Therefore the temprature at the outside windows furface when the heat lost per second doubles is -13.18°C
Answer:
zero or 2π is maximum
Explanation:
Sine waves can be written
x₁ = A sin (kx -wt + φ₁)
x₂ = A sin (kx- wt + φ₂)
When the wave travels in the same direction
Xt = x₁ + x₂
Xt = A [sin (kx-wt + φ₁) + sin (kx-wt + φ₂)]
We are going to develop trigonometric functions, let's call
a = kx + wt
Xt = A [sin (a + φ₁) + sin (a + φ₂)
We develop breasts of double angles
sin (a + φ₁) = sin a cos φ₁ + sin φ₁ cos a
sin (a + φ₂) = sin a cos φ₂ + sin φ₂ cos a
Let's make the sum
sin (a + φ₁) + sin (a + φ₂) = sin a (cos φ₁ + cos φ₂) + cos a (sin φ₁ + sinφ₂)
to have a maximum of the sine function, the cosine of fi must be maximum
cos φ₁ + cos φ₂ = 1 +1 = 2
the possible values of each phase are
φ1 = 0, π, 2π
φ2 = 0, π, 2π,
so that the phase difference of being zero or 2π is maximum
Answer:
2.25 %
Explanation:
65-95-99.7 is a rule to remember the precentages that lies around the mean.
at the range of mean (
) plus or minus one standard deviation (
), ![P([\mu-\sigma \leq X \leq \mu+\sigma])\approx 68.3%](https://tex.z-dn.net/?f=P%28%5B%5Cmu-%5Csigma%20%5Cleq%20X%20%5Cleq%20%5Cmu%2B%5Csigma%5D%29%5Capprox%2068.3%25)
at the range of mean plus or minus two standard deviation, ![P([\mu -2\sigma \leq X \leq \mu+2\sigma])\approx 95.5%](https://tex.z-dn.net/?f=P%28%5B%5Cmu%20-2%5Csigma%20%5Cleq%20X%20%5Cleq%20%5Cmu%2B2%5Csigma%5D%29%5Capprox%2095.5%25)
at the range of mean plus or minus three standard deviation, ![P([\mu - 3\sigma\leq X \leq \mu+3\sigma])\approx 99.7%](https://tex.z-dn.net/?f=P%28%5B%5Cmu%20-%203%5Csigma%5Cleq%20X%20%5Cleq%20%5Cmu%2B3%5Csigma%5D%29%5Capprox%2099.7%25)
So, note that they are asking about the probability that it is greater than 0.32, that is the mean (0.3) plus two times the standard deviation (0.1) (
)
So we know that the 95.5% is between 
and 
, hence approximately the 4.5% (100%-95.5%) is greater than 0.32 or less than 0.28. But half (4.5%/2=2.25%) is greater than 0.32 and the other half is less than 0.28.
So 
Answer: A. Greater than 384 Hz
Explanation:
The velocity of sound is directly related to the temperature rather it is directly proportional meaning if the temperature decreases the velocity decreases and if temperature increases the velocity increases.
Now, we are given that temperature has risen from 20°C to 25°C meaning it has increases. So it implies that velocity must also increase.
Also, the velocity for organ pipe is directly proportional to its frequency. Now if velocity increases frequency must also increase. In this case, the original frequency is 384 Hz. Now increasing the temperature resulted in increase in velocity and thus increase in frequency.
So option a is correct. i.e. now frequency will be greater than 384 Hz.
Answer:
75 m
Explanation:
The horizontal motion of the projectile is a uniform motion with constant speed, since there are no forces acting along the horizontal direction (if we neglect air resistance), so the horizontal acceleration is zero.
The horizontal component of the velocity of the projectile is
and it is constant during the motion;
the total time of flight is
t = 5 s
Therefore, we can apply the formula of the uniform motion to find the horizontal displacement of the projectile:
