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].
Answer:
x=5, y=8
Step-by-step explanation:
x+y=13
2x-y=2
add these two equations
3x=15
therefore x=5
apply this value in x+y=13
5+y=13
then y=13-5 = 8
Answer: The number is 40
Step-by-step explanation:
We will set up an equation where 4/5 is being multiply by the number to get 32. we will represent that number by x
4/5 * x = 32 solve for x
4/5x = 32
0.8x = 32
x = 40
Answer:
Step-by-step explanation:
Null hypothesis should be: The average woman's leg hair grows an eighth of an inch per month: u = eighth of an inch
Alternative hypothesis: The average woman's leg hair growth is not an eighth of an inch per month after treatment: u ≠ eighth of an inch
This test after carrying out its treatment will be able to determine if the drug was effective or not
Answer:
-75
Step-by-step explanation:
Let us consider the first odd number to be 'x'.
Thus:
- 1st odd number: x
- 2nd odd number: x+2
- 3rd odd number: x+3
According to the question, the sum of these three consecutive ODD numbers should be equal to -219
So,
x + x + 2 + x + 4 = -219
3x + 6 = -219
3x = -225
x = -75
