Answer:
C
Step-by-step explanation:
A: Perpendicular lines have 1 solution. A is not the answer.
B: If the lines intersect, there is one solution, not many.
C: The lines are the same or can be reduced to being the same. C is the answer.
D: The lines don't intersect means that the lines are parallel. There isn't a solution.
Mean = it's really just another word for average. You add all the values up together, and divide the sum by the number of values there are. So here :
9 + 13 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9 = 100
And now, you count how many values there are ^ up there. There are 10 values (just count how many numbers there are) and then you have to divide 100 by 10.
100 ÷ 10 = 10
Your MEAN is : 10
Let 9x^2-1 = y^2
<span>=> 18xdx = 2ydy </span>
<span>=> ydy = 9xdx </span>
<span>lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1 </span>
<span>upper limit = sqrt(9*4/9 - 1) = sqrt(3) </span>
<span>Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx </span>
<span>= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1)) </span>
<span>= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y) </span>
<span>=81* Int. [1,sqrt(3)] dy/(y^2+1)^3 </span>
<span>y=tanz </span>
<span>dy = sec^2z dz </span>
<span>=81*Int [pi/4,pi/3] cos^4(z) dz </span>
<span>=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz </span>
<span>=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz </span>
<span>=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) </span>
<span>+ 81/32 *(sin(-pi/3)-sin(pi)) </span>
<span>=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) </span>
<span>=81/32*(pi+3sqrt(3)-8)</span>
