Do you have the answer choices ?
Answer:
225 rpm
Explanation:
The angular acceleration of the fan is given by:

where
is the final angular speed
is the initial angular speed
is the time interval
For the fan in this problem,

Substituting,

Now we can find the angular speed of the fan at the end of the 5th second, so after t = 5 s. It is given by:

where

Substituting,

Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches
Answer:
astronauts age is 32 years
correct option is e 32 years
Explanation:
given data
travels = 20 light year
stay = 2 year
return = 52 years
to find out
astronauts aged
solution
we know here they stay 2 year so time taken in traveling is
time in traveling = ( 52 -2 ) = 50 year
so it mean 25 year in going and 25 years in return
and distance is given 20 light year
so speed will be
speed = distance / time
speed = 20 / 25 = 0.8 light year
so time is
time = 
time = 
time = 15 year
so age is 15 + 2 + 15
so astronauts age is 32 years
so correct option is e 32 years