π is the indicated value of g(1/2) .
Given,
g(1/2)
So,
g(1/2) = [tex]\int\limits^1-h_h{t^-1/2(1-t^-1/2)} \, dt[/tex]
[tex]\int\limits^1_0 {dt/\sqrt{1-t^2} } \,[/tex]
[tex]\int\limits^1_0 {dt/\sqrt{1/4 - (t-1/2)^2[/tex]
[tex]sin^-1(t-1/2/1/2)[/tex]
Put the limits in the above function,
= sin^-1(1) - sin^-1(-1)
= π
Hence the indicated value of g(1/2) is π .
Know more about functions,
https://brainly.com/question/30845151
#SPJ1
Which of the following statements is not true?
Choose the incorrect statement below.
The three-part inequality - 1 <-3x ≤ 1 is equivalent to -5x<
15x2
<3 is equivalent to -6≤5-x<6.
The three-part inequality - 3s-
OD. The three-part inequality -7≤11-x<7 is equivalent to 4 < x≤ 18.
OA.
OB.
C.
The three-part inequality -5s-10x<5 is equivalent to
5-x
...
The incorrect statement is:
B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.
In the given statement, there is an error in the inequality. The correct statement should be:
The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.
When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:
- 5x < 15x^2 and 15x^2 < 3
Simplifying the first inequality:
- 5x < 15x^2
Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:
- 5 < 15x
Simplifying the second inequality:
15x^2 < 3
Dividing by 15, we get:
x^2 < 1/5
Taking the square root (assuming x ≥ 0), we have two cases:
x < 1/√5 and -x < 1/√5
Combining these inequalities, we get:
- 5 < 15x and x < 1/√5 and -x < 1/√5
Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.
For more such questions on inequality
https://brainly.com/question/30681777
#SPJ8
PLS HELP 50 POINTS!!
The line segment FG represent the volume of water decreases in Katherine's water bottle.
From the given graph, x-axis represents the distance from home (km) and the y-axis represents the volume (L).
The line segment FG represent the volume of water decreases in Katherine's water bottle, the line segment HI represent the volume of water increases in Katherine's water bottle and the line segment KL represents there is no change in water level.
Therefore, the line segment FG represent the volume of water decreases in Katherine's water bottle.
To learn more about the graph visit:
brainly.com/question/14375099.
#SPJ1
