Answer:
Third option
Step-by-step explanation:
: ) Hope u will have a great day
Answer:
27 67 16 01 27 35 21 37 74 10
Step-by-step explanation:
Starting from the left, you pick two numbers together and skip two numbers if it is greater than 78.
Meaning:
27816 78416 01822 73521 37741 016312 68000 53645 56644 97892 63408 77919 44575
You pick [27] and leave 81 since it is greater than 78, the population number.
Then you pick [67] and leave 84 as it is also greater than 78.
Then you pick [16] and [01] but leave 82, as it is greater than 78.
Then pick [27], [35], [21], [37], [74] and [10] since they are all less than 78.
At this juncture, you have identified 10 numbers: 27 67 16 01 27 35 21 37 74 10
it is equal to 2 1/2
Step-by-step explanation:
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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>
