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>
Answer: 0.00000565
Step-by-step explanation:
Required to win:
6 number match $10,000
5 number match $ 5,000
4 number match $ 1000
3 number match $ 5,00
2 number match $ 50
1 number match $ 10
Therefore, to win $10,000 ;
All 6 numbers must match
Number of right numbers = 6
Total numbers = 25
Since it is without replacement :
Probability = required outcomes / Total possible outcomes
P(First number match) = 6/25
P(second number match) = 5/24
P(third number match) = 4/23
P(fourth number match) = 3/22
P(fifth number match) = 2/21
P(sixth number match) = 1 / 20
Therefore, Probability of winning $10000 :
(6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (1/20) = 720 / 127512000 = 0.0000056465
= 0.00000565
Answer:
A of the shaded figure is 90cm
Answer:
Option 4 is correct. The length of PR is 6.4 units.
Step-by-step explanation:
From the given figure it is noticed that the triangle PQR and triangle MQR.
Let the length of PR be x.
Pythagoras formula

Use pythagoras formula for triangle PQM.





The value of PM is 10. The length of PR is x, so the length of MR is (10-x).
Use pythagoras formula for triangle PQR.


.....(1)
Use pythagoras formula for triangle MQR.



.... (2)
From equation (1) and (2) we get




Therefore length of PR is 6.4 units and option 4 is correct.
Answer:
x=10°
y = 12°
Step-by-step explanation:
<TSV = 5x + 4x = 90°
=> 9x = 90°
Divide by 9,
x = 10°
<RSU = 10y + 10° + 5x = 180°
=> 10y + 10° + 5*10° = 180°
=> 10y + 10° + 50° = 180°
=> 10y + 60° = 180°
Subtract 60° on both sides,
10y = 180° - 60° = 120°
Divide by 10,
y = 120° / 10 = 12°