Answer:
9.86 inches
Step-by-step explanation:
Given:
The cup will be a right circular cone with:-
Radius, r = 3 inches
Volume of cone = 93 cubic inches
Height of the cup, h = ?
Solution:
<u>By using :-</u>
<u />
By dividing both sides by 9.43
Thus, the cup need to be 9.86 inches taller to hold 93 cubic inches of water.
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.