Answer:
T₂ = 421.4 K
Step-by-step explanation:
The temperature, T, of a given mass of gas varies inversely with its Volume,V.
We have,
V₁ = 98 cm³, T₁ = 28° C = (28+273) K = 301 K
V₂ = 70 cm₃
We need to find the new temperature of the gas. Using the above relation to find T₂.
Hence, the required temperature of the gas is 421.4 K.
Answer:
Step-by-step explanation:
arithmetic sequence formula:
where is the first term and
is the common difference
Given:
⇒
⇒
Given:
⇒
⇒
Rearrange the first equation to make the subject:
a = 32 - 9d
Now substitute into the second equation and solve for
(32 - 9d) + 11d = 106
⇒ 32 + 2d = 106
⇒ 2d = 106 - 32 = 74
⇒ d = 74 ÷ 2 = 37
Substitute found value of into the first equation and solve for
:
a + (9 x 37) = 32
a + 333 = 32
a = 32 - 333 = -301
Therefore, the equation is:
The question in this problem is:
<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>
<em />
First of all, let's name the first variable which is the smaller number. Accordingly, the lager number will be
given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:
So:
1. The sum of 2 consecutive integers can be written as:
2. Nine times the smaller and 5 times the larger can be written as:
Finally, the whole statement:
The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:
The two numbers are: