The first letter can be any one of 26 letters. For each one . . .
The second letter can be any one of 26 letters. For each one . . .
The first digit can be any one of 10 digits. For each one . . .
The second digit can be any one of 10 digits. For each one . . .
The third digit can be any one of 10 digits. For each one . . .
The fourth digit can be any one of 10 digits. For each one . . .
The fifth digit can be any one of 10 digits.
The total number of possibilities is
(26 x 26 x 10 x 10 x 10 x 10 x 10) =
( 26² x 10⁵) = (676 x 100,000) = <em>67,600,000</em> .
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)
Answer:
27/14
Step-by-step explanation:
to divide by a fraction flip the fraction over and multiply
3/7 divided by 2/9
flip 2/9
3/7 times 9/2
just multiply the top and bottoms by each other
27/14
234 pages + 2/3 of 234
234+156 = 390pages
52.5% or it can also be a decimal if needed its 0.525
