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nirvana33 [79]
3 years ago
13

I need help with 6,8,9

Mathematics
1 answer:
olga_2 [115]3 years ago
3 0
Number 6: Every time you add 2.4, so the next number would be 11.1
Number 8: 24 1/2 (The sequence of numbers subtracts 5.5 or 5 1/2 every time.)
Number 9: 29.6 (The sequence of numbers subtracts 7.1 every time)
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The volume V of a gas varies inversely as the pressure P and directly as the temperature A certain gas has a volume of 10 liters
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Answer:

Joint variation states that:

If z is directly proportional to x and inversely proportional to y,

i.e, z \propto x , z \propto \frac{1}{y}

then the equation is in the form: z = k\frac{x}{y} where k is the constant of variation.

From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

i.,e V \propto T , V \propto \frac{1}{P}

by definition of joint variation:

V = k\frac{T}{P}  .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

10 = k\frac{300}{1.5}

Simplify:

10 = 200k

Divide by 200 both sides we have;

k = \frac{10}{200} =\frac{1}{20}

Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.

To find the volume (V);

Now substitute the given data and value of k in [1] we have;

V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4

Therefore, the Volume of a gas is, 4 liters


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