Answer:
x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
Step-by-step explanation:
Solve for x:
-3 + sin(x) + 2 sin^2(x) = 0
The left hand side factors into a product with two terms:
(sin(x) - 1) (2 sin(x) + 3) = 0
Split into two equations:
sin(x) - 1 = 0 or 2 sin(x) + 3 = 0
Add 1 to both sides:
sin(x) = 1 or 2 sin(x) + 3 = 0
Take the inverse sine of both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) + 3 = 0
Subtract 3 from both sides:
x = 2 π n_1 + π/2 for n_1 element Z
or 2 sin(x) = -3
Divide both sides by 2:
x = 2 π n_1 + π/2 for n_1 element Z
or sin(x) = -3/2
Take the inverse sine of both sides:
Answer: x = 2 π n_1 + π/2 for n_1 element Z
or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z
The answer is going to be A) 9:14
He answer is subjective probability. Subjective probability is when it has no prior calculations and the person is just guessing. Theoretical probability is when it’s based on prior calculations. Experimental probability is when you experiment and calculate.
Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
I believe it is 180 megabytes because there are 60 seconds in a minute and 3 times 60 equals 180
