____________________
6(3+a)=18+6a
____________________
You need to put a picture of the graph in the question and I can answer it.
Answer: the number of students that were surveyed is 40
Step-by-step explanation:
Let x = total number of students that were surveyed about their favorite colors
1/4 of the students preferred red.
This means that the number of students that preferred red is 1/4 × x = x/4
1/8 of the students preferred blue.
This means that the number of students that preferred blue is 1/8 × x = x/8
The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes
x - (x/4 + x/8) = x - 3x/8 = 5x/8
3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8
if 15 students prefer green, then
3x/8 = 15
3x = 120
x = 120/3 = 40 students
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].
