Answer:
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Step-by-step explanation:
f(x) = sin (tan^-1 (ln(x)))
u substitution
d/du (sin u) * du /dx
cos (u) * du/dx
Let u =(tan^-1 (ln(x))) du/dx =d/dx (tan^-1 (ln(x)))
v substitution
Let v = ln x dv/dx = 1/x
d/dv (tan ^-1 v) dv/dx
1/( v^2+1) * dv/dx
=1/(ln^2x +1) * 1/x
Substituting this back in for du/dx
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
We know that cos (tan^-1 (a)) = 1/ sqrt(1+a^2)
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Answer:
AP= 12
Step-by-step explanation:
Here is the complete question: If the length of AB=12, what is the length of AP? picture attached.
Given: AB= 12
∠APB= 60°
Remember; sum of all angle of triangle is equal to 180°.
We can look at picture, where two side of triangle is radius of circle.
∴ Angle of two side will also be same for the isosceles triangle.
Lets assume the unknow angle of the triangle be "x".
Now, 
⇒ 2x+60= 180
subtracting both side by 60
⇒ 
∴ 
As now we have all the angle of triangle is 60° (equilateral triangle)
∴ All the side will be same, which is 12
Hence, AP= 12.
Answer:
67
Step-by-step explanation:
The angle with x in it is a vertical angle to the other one labeled & the right angle put together.
Therefore:
48 + 90 = 2x + 4
Solve for x:
138 = 2x + 4
138 - 4 = 2x + (4-4)
134 = 2x
134/2 = 2x/2
X = 67
Hope this helps! Have a great day!
Is this what you are looking for? I hope this helps!
Answer:
c
Step-by-step explanation:
c because 11 and 16 have no GCF other than 1
