The dP/dt of the adiabatic expansion is -42/11 kPa/min
<h3>How to calculate dP/dt in an adiabatic expansion?</h3>
An adiabatic process is a process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression
Given b=1.5, P=7 kPa, V=110 cm³, and dV/dt=40 cm³/min
PVᵇ = C
Taking logs of both sides gives:
ln P + b ln V = ln C
Taking partial derivatives gives:
Substitutituting the values b, P, V and dV/dt into the derivative above:
1/7 x dP/dt + 1.5/110 x 40 = 0
1/7 x dP/dt + 6/11 = 0
1/7 x dP/dt = - 6/11
dP/dt = - 6/11 x 7
dP/dt = -42/11 kPa/min
Therefore, the value of dP/dt is -42/11 kPa/min
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Assuming that :
- The number of the gallons is symbolized by g
- Time per minute is symbolized by t
the equation would be :
g = 10 + 7.5 t
Hope this helps
Answer: 19.8 ft
Step-by-step explanation:
Use the Pythagorean Theorem formula to solve for how high the top of the ladder reach.
The formula says a^2 + b^2 = c^2
Where a and b are the two legs and C is the hypotenuse.
In this situation, the hypotenuse will be length of the ladder , and either a or b will be the length of the ladder from the building or the length of how long the ladder.
a will be 3 , and c will be 20. Input in the values into the formula and solve for b.
3^2 + b^2 = 20^2
9 + b^2 = 400
-9 -9
b^2 = 391
b = 
b = 19.77371 round to the nearest tenth is , 19.8
Answer: B.The cost of rental fee only
Step-by-step explanation:
The $35 is the cost of the rental fee only. The person would then have to pay a further $15 for every hour they use the boat.
Essentially, the $35 is the fixed cost associated with the rental and the $15 is the variable cost to do so. If this were in a linear equation format it would take the form: y = 15x + 35.
Step-by-step explanation:
To solve a system of equations, we can add the two equations and solve for one of the remaining variables -- let's try to eliminate the 
variable when we add the two equations together.
Right now, there's a 
term in the first equation, and a 
term in the second equation, so if we add those together, we'll be able to eliminate the variable altogether and solve for 
.
However, when we also have a 
term in the first equation and 
term in the second equation, so adding these together will also eliminate the term, leaving a 
on the left-hand side of the equation.
If we add the two numbers on the right side of the equation, we get 
, which does not equal , meaning there are no solutions to this system of equations.
