find all solutions of cosx-\sqrt(1-3cos^(2)x)=0 a. 60° + n360°, 300° + n360° b. 30° + n360°, 210° + n360° c. 30° + n360°, 330° + n360° d. 60° + n360°, 120° + n360°

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The equation is:

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

is there a picture

step-by-step explanation: