Answer: F(t) = 11 - 0.9(t)
Explanation:
We know the following:
The candle burns at a ratio given by:
Burning Ratio (Br) = 0.9 inches / hour
The candle is 11 inches long.
To be able to create a function that give us how much on the candle remains after turning it after a time (t). We will need to know how much of the candle have been burned after t.
Let look the following equation:
Br = Candle Inches (D) / Time for the Candle to burn (T) (1)
Where (1) is similar to the Velocity equation:
Velocity (V) = Distance (D)/Time(T)
This because is only a relation between a magnitude and time.
Let search for D on (1)
D = Br*T (2)
Where D is how much candle has been burn in a specif time
To create a function that will tell us how longer remains of the candle after be given a variable time (t) we use the total lenght minus (2):
How much candle remains? ( F(t) ) = 11 inches - Br*t
F(t) = 11 - 0.9(t)
F(t) defines the remaining length of the candle t hours after being lit
Answer:
4. Both points have the same instantaneous angular velocity
Explanation:
Angular velocity is a measure of the the number of rotations per unit time. This does not depend on the radius of the wheel. Hence, all points on the wheel have the same angular velocity. This invalidates option 1.
The centripetal acceleration is given by the product to the square of the angular velocity and the radius or distance from the centre. A and B are located at different distances from the centre. Hence, they have different centripetal acceleration. This invalidates option 2.
The tangential acceleration depends on the linear velocity which itself is a product of the angular velocity and the distance from the centre. Hence, it is different for both points because they are at different distances from the centre.
Since both A and B are fixed points on the wheel, they move through equal angles in the same time. In fact, for any other fixed point, they all move through the same angle in the same time. This invalidates option 5.
Answer:
Epx= - 21.4N/C
Epy= 19.84N/C
Explanation:
Electric field theory
The electric field at a point P due to a point charge is calculated as follows:
E= k*q/r²
E= Electric field in N/C
q = charge in Newtons (N)
k= electric constant in N*m²/C²
r= distance from load q to point P in meters (m)
Equivalences
1nC= 10⁻⁹C
known data
q₁=-2.9nC=-2.9 *10⁻⁹C
q₂=5nC=5 *10⁻⁹C
r₁=0.840m
Calculation of the electric field at point P due to q1
Ep₁x=0
Calculation of the electric field at point P due to q2
Calculation of the electric field at point P(0,0) due to q1 and q2
Epx= Ep₁x+ Ep₂x==0 - 21.4N/C =- 21.4N/C
Epy= Ep₁y+ Ep₂y=36.95 N/C-17.11N =19.84N/C
They'll vibrate at their characteristic resonant frequency. That depends on the material the object is made of and its shape.
