Answer:
1/4 gallon
Step-by-step explanation:
the least number that has at least one x is 1/4
Answer:
incorrect
Step-by-step explanation:
this is because it would be 1/2 and 1/6. you would have to multiply the bases for a probability of 1/12
Let,
the numbers be "x" and "y"
According to the question,
x = 4y ......................................................equation (1)

...................................equation (2)
Taking equation (2)

Substituting the value of "x" from equation (1), we get,





Cross multiplying, we get,


<u />



Now,
Taking equation (1)
x = 4y
Substituting the value of "y", we get

So, the numbers are
and
Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].