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.
Answer:
6
Step-by-step explanation:
6 is a multiple of three with only itself
Answer:
x^3/2 - 6x^1/2
Step-by-step explanation:
f(x) = x - 6
g(x) = x^1/2
g(x) * f(x) = x^1/2(x - 6)
g(x) * f(x) = x^3/2 - 6x^1/2
A. let the distance be d
so we have Δd/Δt=8.8min
Δd= 8.8Δt
d=∫8.8Δt-------(1)
b. d should be positive because the diver is ascending at a positive rate relative to depth
c. d=rt
t=d/r = 32.12/8.8 min
t= 3.65min
