Answer:
θ = 2 π n_1 + π/2 for n_1 element Z or θ = 2 π n_2 for n_2 element Z
Step-by-step explanation:
Solve for θ:
cos(θ) + sin(θ) = 1
cos(θ) + sin(θ) = sqrt(2) (cos(θ)/sqrt(2) + sin(θ)/sqrt(2)) = sqrt(2) (sin(π/4) cos(θ) + cos(π/4) sin(θ)) = sqrt(2) sin(θ + π/4):
sqrt(2) sin(θ + π/4) = 1
Divide both sides by sqrt(2):
sin(θ + π/4) = 1/sqrt(2)
Take the inverse sine of both sides:
θ + π/4 = 2 π n_1 + (3 π)/4 for n_1 element Z
or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z
Subtract π/4 from both sides:
θ = 2 π n_1 + π/2 for n_1 element Z
or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z
Subtract π/4 from both sides:
Answer: θ = 2 π n_1 + π/2 for n_1 element Z
or θ = 2 π n_2 for n_2 element Z
If you divide both by 11, you get 7/9. 7/9 is the fraction in simplest form.
A squared + b squared = c squared
Answer:
x > 1.7 minutes
The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.
Step-by-step explanation:
The two plans must be defined by the equation of the line y = mx + b, where
y = plan
m = slope or payment of additional cents per minute
x = time expressed in minutes
For Plan A, we have
y = 4x + 40.10 (Equation A)
While plan B is defined as
y = 7x + 35 (Equation B)
Plan A must be less than Plan B,
4x + 40.10 < 7x + 35
We put the “x” on the left side and the independent terms on the right side,
4x - 7x < 35 - 40.10
We add algebraically,
-3x < -5.10
We multiply the equation by -1 to eliminate the two “minus” signs, changing the inequality sign,
3x > 5.10
We isolate x,
x > 5.10 / 3
We solve, calculating the value of x,
x > 1.7 minutes
The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.
Answer:
3(x - a)(x - b)(x - c) when a + b + c = 3x .
Step-by-step explanation:
i don't know but this has to be right
