F(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
= ln³x/3 +C with C is constant
In addition, we have f(2)=6, so we have 6=ln³2/3+C
or C= 6- <span>ln³2/3
And f(x)= </span>ln³x/3+ <span> 6- </span><span>ln³2/3</span>
Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
The answer that you said is right. I totally agree with you.
Answer:
23) 53/100
24)2/5
25)3/5
26)11/50
27)17/50
28)19/1000
29)4/5
30)1/250
31)9/25
32)1 3/10
33)11 1/2
34) 7 3/40
Step-by-step explanation: Hope this helps!
Reflection over x-axis
hope that helps
