Answer:
Explanation:
given equation
aA + bB + C = 0
Putting the given values
a(6i-8j) +b (-8i-3j) +(26i-19j) = 0
i ( 6a - 8b ) - j ( 8a + 3 b ) = - 26 i + 19 j
comparing the coefficients of i and j
6a - 8b = -26
8a + 3b = -19.
multiplying first equation by 4 and second equation by 3
24a - 32 b = - 104
24a + 9b = -57
9b + 32b = -57 + 104
41 b = 47
b = 1.41
6 a - 8 x 1.41 = -26
6a = -14.72
a = - 2.45
Answer:
The energy of the wave is 1.435 x 10⁻⁴ J
Explanation:
Given;
area of the window, A = 0.5 m²
the rms value of the field, E = 0.06 V/m
The peak value of electric field is given by;
The average intensity of the wave is given by;
The average power of the wave is given by;
P = I x A
P = (9.569 x 10⁻⁶ W/m²) (0.5 m²)
P = 4.784 x 10⁻⁶ W
The energy of the wave is given by;
E = P x t
E = (4.784 x 10⁻⁶ W)(30 s)
E = 1.435 x 10⁻⁴ J
Therefore, the energy of the wave is 1.435 x 10⁻⁴ J
At the vertex, it's vertical velocity is 0, since it has stopped moving up and is about to come back down, and its displacement is 0.33m.
So we use v² = u² + 2as (neat trick I discovered just then for typing the squared sign: hold down alt and type 0178 on ur numpad wtih numlock on!!!) ANYWAY.......
We apply v² = u² + 2as in the y direction only. Ignore x direction.
IN Y DIRECTION:
v² = u² + 2as
0 = u² - 2gh
u = √(2gh) (Sub in values at the very end)
So that will be the velocity in the y direction only. But we're given the angle at which the ball is hit (3° to the horizontal). So to find the velocity (sum of the velocity in x and y direction on impact) we can use: sin 3° = opposite/hypotenuse = (velocity in y direction only) / (velocity)
So rearranging,
velocity = (velocity in y direction only) / sin 3°
= √(2gh)/sin 3°
= (√(2 x 9.8 x 0.33)) / sin 3°
= 49 m/s at 3° to the horizontal
Explanation:
Earth or any planet are actually born from huge clouds of gas and dust. Their stellar mass are fairly distributed at a radius from the axis of rotation. Gravitational force cause the cloud to come together. Now the whole gathered in smaller area. Now, individual particles come close to the roational axis. Thus, decreasing the moment of inertia of the planet.
As
I=mr^2
reducing r reduces I. However, the angular moment of the system remains always conserved. So, to conserve the angular momentum the angular velocity of the planet increases and so did the otational kinetic energy
Answer:
About 133 db.
Explanation:
Sound Intensity Level in db (SIL db) is equal to 10log (base 10) times the ratio of the sound intensity at 200 watts (I) relative to the sound intensity of the reference sound intensity (I sub 0), which by default is equal to 10⁻¹² W/m² or 0 dB.
I = 200 w / 10 m^2 = 20 w per square meter
I sub 0 = 10^-12 w per square meter
SIL = 10log ( I / I sub o) = 20 / 10^-12 = 10log ( 20^12) = 10 ( 13.3 ) = 133 db
Hope I typed this part correctly. Hard to get it in without being able to do exponents, etc. :D
