Given:
A number is q, multiply it by 2 and add 5.
You get the same answer as when you minus 2 from q.
To find:
The value of q.
Solution:
The algebraic representation of the statement "a number is q, multiply it by 2 and add 5" is
Multiply q by 2 = 2q
Multiply q by 2 and then add 5 : 2q + 5
So, the first result is 2q+5.
When you minus 2 from q = q-2
So, the second result is q-2.
According to the question, both results are equal. Equate both results to get the value of q.
Isolate variable terms.
Therefore, the value of q is -7.
Newton's Law of Cooling states that the change
of the temperature of an object is proportional to the difference between its
own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent
to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the
temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
I know 8-10.
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