Answer:
Explanation:
i = Imax sin2πft
given i = 180 , Imax = 200 , f = 50 , t = ?
Put the give values in the equation above
180 = 200 sin 2πft
sin 2πft = .9
sin2π x 50t = .9
sin 360 x 50 t = sin ( 360n + 64 )
360 x 50 t = 360n + 64
360 x 50 t = 64 , ( putting n = 0 for least value of t )
18000 t = 64
t = 3.55 ms .
Answer:
Explanation:
b ) First is concave lens with focal length f₁ = - 12 cm .
object distance u = - 20 cm .
Lens formula
1 / v - 1 / u = 1 / f
1 / v + 1 / 20 = -1 / 12
1 / v = - 1 / 20 -1 / 12
= - .05 - .08333
= - .13333
v = - 1 / .13333
= - 7.5 cm
first image is formed before the first lens on the side of object.
This will become object for second lens
distance from second lens = 7.5 + 9 = 16.5 cm
c )
For second lens
object distance u = - 16.5 cm
focal length f₂ = + 12 cm ( lens is convex )
image distance = v
lens formula ,
1 / v - 1 / u = 1 / f₂
1 / v + 1 / 16.5 = 1 / 12
1 / v = 1 / 12 - 1 / 16.5
= .08333- .0606
= .02273
v = 1 / .02273
= 44 cm ( approx )
It will be formed on the other side of convex lens
distance from first lens
= 44 + 9 = 53 cm .
magnification by first lens = v / u
= -7.5 / -20 = .375 .
magnification by second lens = v / u
= 44 / - 16.5
= - 2.67
d )
total magnification
= .375 x - 2.67
= - 1.00125
height of final image
= 2.50 mm x 1.00125
= 2.503mm
e )
The final image will be inverted with respect to object because total magnification is negative .
Answer:
The radius is decreasing at 4 mm/s
Explanation:
The volume of a sphere is:
So, when the volume is 972π mm^3 the radius r is:
r = 9mm
Now, the change rate is given by the derivative:
Where: dV/dt = -324π mm^2/s
r = 9mm
Solving for dr/dt:
dr/dt = -4mm/s
Answer: 7022.2kg/m³, yes, I was cheated
Explanation:
Density of an object is defined as the ratio of the mass of the object to its volume. Mathematically;
Density = Mass/Volume
Note that the unit of both mass and volume must be standard unit.
Given mass = 0.0158kg
Dimension of the metal = 5mm×15mm×30mm
Note that 1mm = 0.001m
The volume of the metal will be
0.005×0.015×0.03
= 0.00000225m³
Density = 0.0158/0.00000225
Average density of the metal = 7022.2kg/m³
Since the standard density of Gold is 19,320kg/m³ and is higher than the density prescribed for me, it shows the I was cheated.
Answer:
Explanation:
If a particle move with time and expressed according to the formula:
f(t) = 0.01t⁴ − 0.03t³
a) Velocity is the change in motion of the particle with respect to time and it is expressed as;
Hence the velocity of the particle at time t is 
b) To calculate the velocity after 1 second, we will substitute t = 1 into the function v(t) in (a) as shown:
Hence the velocity after 1second is -0.05
c) The particle is at rest when when the time is zero.
Initially, the body is not moving and the time during this time is 0. Hence the particle is at rest when t = 0second
