Part A
To identify the values of x that make 2x−1 positive
⇒ 2x - 1 > 0
⇒ 2x > 1
⇒ x > 
As a result, for any x greater than
, the expression 2x-1 is positive
Part B
To find values of y making 21−37 negative
⇒ 21-3y < 0
⇒ 21 < 3y
⇒ 7 < y
Thus, for all y values exceeding 7, the expression 21-3y is negative
Part C
To identify values of c that digit 5−3c greater than 80
⇒ 5-3c > 80
⇒ -3c > 75
⇒ -c > 25
⇒ c < -25
Therefore, for values of c less than -25, the expression 5-3c surpasses 80
Answer:
Step-by-step explanation:
Considering the equation
Sin(5x) = ½
5x = arcSin(½)
5x = 30°
Then,
The general formula for sin is
5θ = n180 + (-1)ⁿθ
Dividing throughout by 5
θ = n•36 + (-1)ⁿ30/5
θ = 36n + (-1)ⁿ6
The solution range is
0<θ<2π which means 0<θ<360
First solution
When n = 0
θ = 36n + (-1)ⁿθ
θ = 0×36 + (-1)^0×6
θ = 6°
When n = 1
θ = 36n + (-1)ⁿ6
θ = 36-6
θ = 30°
When n = 2
θ = 36n + (-1)ⁿ6
θ = 36×2 + 6
θ = 78°
When n =3
θ = 36n + (-1)ⁿ6
θ = 36×3 - 6
θ = 102°
When n=4
θ = 36n + (-1)ⁿ6
θ = 36×4 + 6
θ = 150
When n=5
θ = 36n + (-1)ⁿ6
θ = 36×5 - 6
θ = 174°
When n = 6
θ = 36n+ (-1)ⁿ6
θ = 36×6 + 6
θ = 222°
When n = 7
θ = 36n + (-1)ⁿ6
θ = 36×7 - 6
θ = 246°
When n =8
θ = 36n + (-1)ⁿ6
θ = 36×8 + 6
θ = 294°
When n =9
θ = 36n + (-1)ⁿ6
θ = 36×9 - 6
θ = 318°
When n =10
θ = 36n + (-1)ⁿ6
θ = 36×10 + 6
θ = 366°
When n = 10 surpasses the θ range
Thus, the solutions range from n =0 to n=9
Therefore, there are 10 solutions within the interval 0<θ<2π
The hyperbolic cosine function (cosh) is defined as
cosh (x) = (e^x + e^-x) / 2
The tangent line's slope at any given point on a function is determined by the derivative of that function at that specific point.
d/dx [cosh(x)] = d/dx[(e^x + e^-x) / 2] = (e^x - e^-x) / 2 = sinh(x)
Assuming the slope equals 2, we have
sinh(x) = 2
thus,
x = sinh^-1 (2) = 1.444
Consequently, the curve of y = cosh(x) has a slope of 2 at the coordinate x = 1.44
1. According to the definition, a specific point that splits a line segment into a ratio of a:b is indicated by the following x-coordinate:
And the y-coordinate:
2. Keeping this in mind, you have:
A) x-coordinate:
y-coordinate:
The answer is: 
B) The x-coordinate is:
The y-coordinate is:
The answer is: 
The corresponding Venn Diagram for this issue is depicted below
P(E|F) and P(F|E) denote the conditional probabilities.
P(E|F) is calculated as P(E∩F) ÷ P(F) = ¹/₂ ÷ ¹/₂ = 1
P(F|E) is determined by P(F∩E) ÷ P(E) = ¹/₂ ÷ ¹/₂ = 1
