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Liono4ka [1.6K]
3 years ago
8

Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?

Mathematics
1 answer:
Korolek [52]3 years ago
5 0
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>
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Haha, you first start off with adding 3 to both sides, cancelling the -3, and adding it to 9. you end up with 5x=12, in which you divide both sides by 5. you get 2 and 2/5 or 12/5! hope that helps :)
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3 years ago
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masya89 [10]

Answer:

Part A = the middle one

Part B = 4 days

Step-by-step explanation:

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325 x 4 = 1,300

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After releasing of radioactive material into.The atnosphere from.A nuclear.Powe plant in a country in 1988, the hay in that coun
Radda [10]

Answer:

the question is incomplete, so I looked for a similar one:

<em>After the release of radioactive material into the atmosphere  from a nuclear power plant, the hay was contaminated by iodine  131 ( half-life, 8 days). If it is all right to feed the hay to cows  when 10% of the iodine 131 remains, how long did the farmers  need to wait to use this hay? </em>

iodine's half life (we are given x, we need to find b):

0.5A₀ = A₀eᵇˣ

x = 8 days

we eliminate A₀ from both sides

0.5 = eᵇ⁸

ln 0.5 = ln eᵇ⁸

-0.69315 = b8

b = -0.69315 / 8 = -0.08664

since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):

0.1A₀ = A₀eᵇˣ

0.1 = eᵇˣ

ln 0.1 = bx

where b = -0.08664

x = ln 0.1 / -0.08664  = -2.302585 / -0.08664  = 26.58 days

4 0
3 years ago
Is andies solution correct
Nadusha1986 [10]
The solution is correct.
3 0
3 years ago
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