What is the probability of spinning a number less than 3 or6
1 answer:
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At first we need to know how to find the distance between two parallel lines
The parallel lines which have the same slope
If we have two parallel lines ⇒ y₁ = mx + c₁ and y₂ = mx + c₂
So, the distance between y₁ and y₂ = d =
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Part (1):
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<span>The distance between the lines
</span>
<span> Y₁ = 3x + 10 and Y₂ = 3x - 20</span>
∴ m = 3 , c₁ = 10 and c₂ = -20
∴ d =
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Part (2):
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<span>The distance between the lines
</span>
Y₁ = <span>3/2 x + 3/2</span> and Y₂ = <span>3/2 x - 5</span>
∴ m = 3/2 = 1.5 , c₁ = 3/2 = 1.5 and c₂ = -5
∴ d =
The parallel lines which have the same slope
If we have two parallel lines ⇒ y₁ = mx + c₁ and y₂ = mx + c₂
So, the distance between y₁ and y₂ = d =
========================================================
Part (1):
=======
<span>The distance between the lines
</span>
<span> Y₁ = 3x + 10 and Y₂ = 3x - 20</span>
∴ m = 3 , c₁ = 10 and c₂ = -20
∴ d =
========================================================
Part (2):
=======
<span>The distance between the lines
</span>
Y₁ = <span>3/2 x + 3/2</span> and Y₂ = <span>3/2 x - 5</span>
∴ m = 3/2 = 1.5 , c₁ = 3/2 = 1.5 and c₂ = -5
∴ d =
Hi!
Let's first expand the cotangent of theta.
You'll probably know that tangent will be "y/x", or , and cotangent is the reciprocal of this, meaning that it is "x/y" or
.
That means that we are now given this equation.
That'll multiply to:
We'll want a common denominator to add by multiplying to both top and bottom of the second term:
Pythagorean Identity states that , so substitute that in:
Which simplifies to:
Hope this helps!