Recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
Then we can write
sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)
Then
∫ sin(9x) cos(9x) dx
= 1/2 ∫ sin(18x) dx
= -1/2 • 1/18 cos(18x) + C
= -1/36 cos(18x) + C
though you could continue with another double angle identity,
cos(2x) = cos²(x) - sin²(x)
to rewrite the antiderivative as
= -1/36 (cos²(9x) - sin²(9x)) + C
= 1/36 (sin²(9x) - cos²(9x)) + C
Answer:
B
Step-by-step explanation:
9 out of 36 chose country, that is expressed as a fraction
= 
Thus calculate this fraction of 240
× 240 = 
= 60 → B
X = 40/30 × 7
x = 280/30
x = 28/3
Answer:
Ratio of the perimeters =3:1
Step-by-step explanation:
We have given that : Ratio of the sides of two squares is 3:1
To find : Ratio of their perimeters
Solution : Let the length of the sides are 3:1 = 3x : x
Formula of perimeter of square = 4(side)
Using the formula ,
Perimeter of 1 square = 4×3x= 12x
Perimeter of 2 square = 4×x= 4x
Ratio of the perimeter of 1 square and 2 square = 12x : 4x
= 3 : 1
Answer:
3300 people
Step-by-step explanation:
There are 1000 households in a town. Specifically, there are
100 households with one member
= 100 × 1 member
= 100 people
200 households with 2 members
= 200 × 2 members
= 400 people
300 households with 3 members
= 300 × 3 member
= 900 people
200 households with 4 members,
= 200 × 4 members
= 800 people
100 households with 5 members
= 100 × 5 members
= 500 people
100 households with 6 members.
= 100 × 6 member
= 600 people
Thus, the total number of people living in the town is
100 people + 400 people + 900 people + 800 people + 500 people + 600 people
= 3300 people
