Answer:
90/150
3/5
Step-by-step explanation:
Answer:
θ = 60° or θ = 120°, which in radians is equivalent to θ = π/3 rad or θ = 2π/3 rad.
Explanation:
The given equation is sin θ = (√3)/2
Solving that equation is finding the value of the angle, θ, whose sine is (√3)/2.
The function that returns the value of the angle whose sine is (√3)/2 is the inverse function of the sine and it has a special name: arc sine or arcsin.
Hence, θ = arcsin (√3)/2.
You can use your knowledge of the notable angles to solve for that equation.
1) The function sine is positive in first and second quadrants.
2) The angles in the first quadrant go from 0° to 90°.
3) The sine of 60° (√3)/2, Hence the first value of θ is 60°
4) The angles in the second quatrant go from 90° to 120°. 60° is the reference angle in the second quadrant, and the angle searched is
- 180° - reference angle = 180° - 60° = 120°. So, 120° is the other solution of the equation.
5) You can convert both angles to radians using the equivalence
- π radians = 180° ⇒ 1 = π rad / 180°
- 60° = 60° × π rad / 180° = π/ 3 rad
- 120° = 120° × π rad / 180° = 2π/3 rad
6) You can verify that sin 60° = (√3)/2 = sin 120° .
Answer: 95/144
Explanation:
There are 12 light bulbs.
There are 5 defective bulbs.
There are 7 not defective bulbs.
P (at least one defective) = first one defective or second one defective or both defective.
P (at least one defective) = (5/12)(7/12) + (7/12)(5/12) + (5/12)(5/12) = 95/144
The point-slope form the line which has the value of slope -5 and contains a point as A(2,-1) is (y+1)=-5(x-2).
<h3>What is point slope form?</h3>
The point slope form of a line is the expression of line which has a specified slope and passes through a point.
The point slope form is givne as,
(y-y₁)=m(x-x₁)
Here, m is the slope of the line, x₁ is the x coordinate of the point by which line passes and y₁ is the y coordinate of the same point.
The slope of a line is -5. This line contains the point A (2,-1). Thus, the point slope form is,
(y-y₁)=m(x-x₁)
(y-(-1))=-5(x-2)
(y+1)=-5(x-2)
Thus, the point-slope form the line which has the value of slope -5 and contains a point as A(2,-1) is (y+1)=-5(x-2).
Learn more about the point slope form here;
brainly.com/question/6497976
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