Ask question

Ask question

All categories

3 years ago

6

The temperature T of a given mass of gas varies inversely with its volume V. The temperature of 90 cm^3 of a certain gas is 25°C

. What will the temperature of the gas be when it is compressed to a volume of 20 cm^3?
a. 112.5°C
b. 6°C
c. 54°C
d. 120°C

1 answer:

Simora [160]3 years ago

4 0

Answer:

A. 112.5°C

Step-by-step explanation:

Use the inverse variation equation, y = $\frac{k}{x}$

Replace y with T, and replace x with V:

T = $\frac{k}{V}$

Plug in 90 as T and 25 as V, then solve for k:

T = $\frac{k}{V}$

90 = $\frac{k}{25}$

2250 = k

So, the equation is T = $\frac{2250}{V}$

Plug in 20 as V and solve for T:

T = $\frac{2250}{V}$

T = $\frac{2250}{20}$

T = 112.5

So, the temperature will be A. 112.5°C

You might be interested in

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago

This is the table i need help with

Papessa [141]

2.3 is the other length
Hope this helps :)

8 0

2 years ago

Read 2 more answers

Simplify 2 to the 5 power to the fourth power over 3 to the second power

melisa1 [442]

I'm assuming you mean 2^(5)(4/3)(2).
So multiplying all of the powers together yields 2^(40/3)

4 0

3 years ago

Which is smaller-21/35, 7/5

Paladinen [302]

Answer:

-21/35

Step-by-step explanation:

So, 7/5 is a postive number, since it doesn't have a negative - sign in front of it. On the other hand, -21/35 does. Knowing this, we can conclude that -21/35 is smaller than 7/5.

If you want another way of thinking about it, just guessing, what is 7/5? Well, 7 is bigger than 5, so it must be at least 1. On the other hand, with -21/35, the -21 doesnt look like its bigger than 35, so it must be smaller than 1.

Answer:

<u>-21/35 is smaller than 7/5 </u>

<u></u>

<u>Ti⊂k∫∈s ω∅∅p</u>

3 0

3 years ago

Read 2 more answers

Please PLEASE please!!! Any math experts can solve these I will give thanks and mark thank you!!!!

Alla [95]

Answer:

8.

numerator: 3

denominator: 2

9.

numerator: 2

denominator: 2

10.

numerator: 2

denominator: 4

6 0

3 years ago