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2 years ago

How many rational numbers lie between any two fractions?

Mathematics

1 answer:

ZanzabumX [31]2 years ago

7 0

Answer:

Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of qp where p and q are integers and q =0.

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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

I need help ASAP!!<br>Mathematics

Ilia_Sergeevich [38]

Answer:AGC and DGH are opposite angles.

Step-by-step explanation:

So, Y+10=3x-40

Y-3x=-50-(1)

3x-40=2x

3x-2x=40

x=40

Y-3x40=-50

y-120=-50

y=-50+120

y=70

Hence, the answer is A 70°

3 0

2 years ago

The cost of toilet paper is 9.99 for 9 rolls, what is the price per roll of toilet paper?

vampirchik [111]

Answer:

$1.11

Step-by-step explanation:

Find the price per roll by dividing the cost by the number of rolls:

9.99/9

= 1.11

So, the price per roll of toilet paper is $1.11

5 0

2 years ago

Read 2 more answers

PLEASE HELP AND SHOW ALL STEPS

Alja [10]

Combining the like terms, the simplified polynomials are given as follows:

a) 4x² - 14x + 17

b) -5x² - 20x + 8

<h3>How are polynomials simplified?</h3>

Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.

Item a:

4(x - 2)(x + 1) - 5(2x - 5)

Applying the distributive property:

4(x² - x - 2) - 10x + 25

4x² - 4x - 8 - 10x + 25

Combining the like terms:

4x² - 4x - 10x - 8 + 25

4x² - 14x + 17

Item b:

-5(x + 2)² + 28

-5(x² + 4x + 4) + 28

-5x² - 20x - 20 + 28

-5x² - 20x + 8

More can be learned about the simplification of polynomials at brainly.com/question/24450834

#SPJ1

4 0

1 year ago

1. There are two differnt maps of Ohio. The scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati i

xeze [42]

Answer:

1. 0.8 cm

2. 1.6 cm

Step-by-step explanation:

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

$\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8$

Hene, 0.8 centimeters would be the distance in 2nd map

A scale of 1:50 means 1 cm equal 50 cm

So, 0.8m would be

0.8 * 100 = 80 cm

Hence, 80 cm would be represented by 80/50 on the map, that is:

$\frac{80}{50}=1.6$

That is 1.6 centimeters

7 0

2 years ago

How many rational numbers lie between any two fractions?​

How many rational numbers lie between any two fractions?