Answer:
(a) 152.85 Nm
(b) 1528.5 Nm
Explanation:
According to the formula of power
P = τ ω
ω = 2 π f
(a) f = 2500 rpm = 2500 / 60 = 41.67 rps
So, 40 x 1000 = τ x 2 x 3.14 x 41.67
τ = 152.85 Nm
(b) f = 250 rpm = 250 / 60 = 4.167 rps
So, 40 x 1000 = τ x 2 x 3.14 x 4.167
τ = 1528.5 Nm
Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Explanation:
v = wavelength x frequency
330 = 5 . 10-² m x f
f = 6600 Hz
the frequency that human can hear is about 20 Hz - 20000 Hz
so human can hear the note.
<h2>
Answer:</h2>
1000th multiple of the standard reference level for intensities.
<h2>
Explanation:</h2>
The sound intensity level (β), measured in decibels, of a sound with an intensity of I is defined as follows;
β = 10 log (I / I₀) --------------------(i)
Where;
I₀ = reference intensity
Given from the question;
β = sound level = 30dB
Substitute this value into equation (i) as follows;
30 = 10 log (I / I₀)
Divide both sides by 3;
3 = log (I / I₀)
Take antilog of both sides;
10^(3) = (I / I₀)
1000 = I / I₀
Solve for I;
I = 1000I₀
Therefore the intensity of the sound is 1000 times the standard reference level for intensities (I₀)
The Kepler mission is specifically designed to survey a portion of our region of the Milky Way galaxy<span> to discover dozens of Earth-size planets in or near the </span>habitable zone<span> and determine how many of the billions of stars in our galaxy have such planets</span>
