What is the rate of change? the second 1 and second 4?
1 answer:
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Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
The value of h(t) when is 10.02.
Solution:
Given function
To find the value of h(t) when :
Substitute in the given function.
Now multiply the common terms into inside the bracket.
Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.
To make the denominator same, take LCM of the denominators.
LCM of 64 and 32 = 64
= 10.02
Hence the value of h(t) when is 10.02.