Answer: 46.90mins
Step-by-step explanation:
The given data:
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet/min.
Solution:
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon
= 4/3 × 3.14 × 55³
= 696556.67 ft³
When the volume 2/3 the maximum volume
= 2/3 × 696556.67 ft³
= 464371.11 ft³
The radius, r₂ at the point is
= 4/3·π·r₂³
= 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4
= 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the
above length
Time taken for the radius to increase the length.
= is 70.369 ft/(1.5 ft/min)
= 46.90 minutes
46.90mins is the time taken to inflate the balloon.
Substitute 
, so that 
. Then the ODE is equivalent to
which is separable as
Split the left side into partial fractions,
so that integrating both sides is trivial and we get
Given the initial condition 
, we find
so that the ODE has the particular solution,
Ok. Something times 90 = 7200.
Let something = x
90x = 7200
Divide both sides by 90.
90x/90 = 7200/90
x = 80
The other factor is 80.
Answer:
- a. 1 / 13
- b. 3 / 13
- c. 10 / 13
Step-by-step explanation:
<h3>a.</h3>
There are four 5's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 5. This means that the probability will be:
<h3>
b.</h3>
For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:
The total possible cards are, still, 52, so, the probability will be
<h3>
c.</h3>
We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face car its:
so
but, we know that
so
