The sum of a rational number and a irrational number

A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per

Tems11 [23]

Answer:

The pressure is changing at $\frac{dP}{dt}=3.68$

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ and we want to find at what rate is the pressure changing.

The equation that model this situation is

$PV^{1.4}=k$

Differentiate both sides with respect to time t.

$\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\$

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

Apply this rule to our expression we get

$V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0$

Solve for $\frac{dP}{dt}$

$V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}$

when P = 23 kg/cm2, V = 35 cm3, and $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ this becomes

$\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}\\\\\frac{dP}{dt}=\frac{-1.4\cdot 23 \cdot -4}{35}}\\\\\frac{dP}{dt}=3.68$

The pressure is changing at $\frac{dP}{dt}=3.68$ .

7 0

3 years ago

A hypothetical population consists of eight individuals ages 13, 14, 17, 20, 21, 22, 24, & 30 years.

Alika [10]

Complete Question

A hypothetical population consists of eight individuals ages 13 14 17 20 21 22 24 30 years.

A: what is the probability that a person in this population is a teenager?

B: what is the probability of selecting a participant who is at least 20 years old?

We have that probability that a person in this population is a teenager and probability of selecting a participant who is at least 20 years old is

From the question we are told

A hypothetical population consists of eight individuals ages 13, 14, 17, 20, 21, 22, 24, & 30 years.

P(T)=0.38
P(T')=0.63

a)

Generally the equation for the probability that a person in this population is a teenager is mathematically given as

$P(T)=\frac{no of teens}{n}\\\\P(T)=\frac{3}{8}$

P(T)=0.38

b)

Generally the equation for the probability of selecting a participant who is at least 20 years old is mathematically given as

$P(T)=\frac{ participants\ who\ is\ at\ least\ 20\ years old}{n}\\\\P(T)=\frac{5}{8}$

P(T')=0.63

For more information on this visit

brainly.com/question/11234923?referrer=searchResults

6 0

2 years ago

The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base

Dmitriy789 [7]

Since the area of a triangle is in the form
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12

6 0

3 years ago

Pls help i might give brainliest

zmey [24]

Answer:

60% I hope I help :) have a great day

6 0

3 years ago

Please help me find the area and perimeter of this composite figure.

pentagon [3]

Answer:

the area is 26 the perimetier is 52

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The sum of a rational number and a irrational number​

The sum of a rational number and a irrational number