Five hundred twenty-five and forty-eight thousandths
Answer:
75 boys
Step-by-step explanation:
Formula-Girls:Boys=Girls:Boys
5:6=_:90
90×5=450
450÷6=75
This is your answer and for the multiplication I gave it to you step by step
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
When the first number increases by one the second number is added by 4's. So from the first part to the second it added 4 then from the 2nd to the 3rd it skips adding 8 to then just add 12. Then from the 3rd to the 4th it skips adding 16 and adds 20. So the next set of numbers would be (4,64) because it skips adding the 24 and adds the 28.
Hope this helps and is not to confusing :)
