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Stolb23 [73]
3 years ago
7

Find the geometric mean of 7 and 9

Mathematics
1 answer:
charle [14.2K]3 years ago
3 0

Answer:

\large\boxed{3\sqrt7}

Step-by-step explanation:

\text{Geometric mean:}\\\\\underbrace{\sqrt[n]{a_1\cdot a_2\cdot a_3\cdot...\cdot a_n}}_n\\\\\sqrt{7\cdot9}=\sqrt{9}\cdot\sqty7=3\sqrt7

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The pressure and volume of an expanding gas are related by the formula PV^b=C, where b and C are constants (this holds in adiaba
bazaltina [42]

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:

\frac{1}{P}\frac{∂P}{∂t}  + \frac{b}{V}\frac{∂V}{∂t} = 0

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

Learn more about adiabatic expansion on:

brainly.com/question/6966596

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4 0
1 year ago
ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately no
dimaraw [331]

Answer: 5.37

Step-by-step explanation:

Let x =  ACT scores.

Given: ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately normal.

i.e. P(X>28)=0.09   (i)

Now,

P(X>28)=P(\dfrac{X-\mu}{\sigma}>\dfrac{28-20.8}{\sigma})\\\\= P(z>\dfrac{7.2}{\sigma})\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]    (ii)

One -tailed z value for p-value of 0.09 =1.3408 [By z-table]

From (i) and (ii)

\dfrac{7.2}{\sigma}=1.3408\\\\\Rightarrow\ \sigma=\dfrac{7.2}{1.3408}\\\\\Rightarrow\ \sigma=5.37

Hence, the standard deviation = 5.37

5 0
3 years ago
Write each expression using n as your variable.
frozen [14]
C3=n
N x 2 - 6 + 2
N < (6x8) - 10
8 0
2 years ago
Simplify the expression -2+6.45z-6+(-3.25z)
erik [133]

Answer:

-8 + 3.2z

Step-by-step explanation:

  1. when there is a "+" in front of an expression in parentheses, the expression remains the same
  2. -2 + 6.45z - 6 - 3.25z
  3. calculate the difference

-8 + 6.45z - 3.25z

collect like terms

-8 + 3.2z

8 0
3 years ago
-5(4+2x)-14x simplify the expression
siniylev [52]

Answer:

− 20 − 24 x

Step-by-step explanation:

simplify

6 0
2 years ago
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