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Verizon [17]
3 years ago
8

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2x^2+8x-1=0

Mathematics
1 answer:
BabaBlast [244]3 years ago
4 0
Divide given eq. by -2, we get, x^2-4x+0.5=0. Here a=1, b=-4 and c=0.5. As disccriminant is given by sqrt(b^2-4*a*c).so sqrt((-4)^2-4*1*0.5)=3.7417.
Real roots are x1,2=-b+-discriminant
x1=-4+3.7417=-0.2583 and x2=-4-3.7417=-7.7417
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What coordinates on the unit circle are associated with the angle measure?
Varvara68 [4.7K]

The tangent of the given angles are the ratios <em>y</em> to the <em>x</em> coordinate of

the point of the terminal side on the unit circle.

The correct options are;

  • \dfrac{34 \cdot \pi}{3} \Longleftrightarrow \underline{ \left(-\dfrac{1}{2}, \ -\dfrac{\sqrt{3} }{2} \right)}

  • -\dfrac{7 \cdot \pi}{4} \Longleftrightarrow \underline{ \left(\dfrac{\sqrt{2} }{2}, \ \dfrac{\sqrt{2} }{2} \right)}

  • 210^{\circ} \Longleftrightarrow \underline{ \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)}

<h3>How to find the points on the unit circle</h3>

The tangent of an angle is given as follows;

tan (\theta) = \mathbf{ \dfrac{Opposite}{Adjacent}} = \dfrac{\Delta y}{\Delta x}

First angle

An angle given is; \mathbf{\dfrac{34 \cdot \pi}{3}}

Therefore;

tan \left(\dfrac{34 \cdot \pi }{3} \right) = \mathbf{ \sqrt{3}}

The above result can be obtained as follows;

\sqrt{3}  = \mathbf{ \dfrac{-\dfrac{\sqrt{3} }{2} }{-\dfrac{1}{2} }}

Which is obtained when we have;

\left( \Delta x, \, \Delta y\right) = \mathbf{\left(-\dfrac{1}{2}, \, -\dfrac{\sqrt{3} }{2} \right)}

Therefore

The required coordinates is therefore;

  • \dfrac{34 \cdot \pi}{3} \Longleftrightarrow \left(-\dfrac{1}{2} , \ -\dfrac{\sqrt{3} }{2} \right)

Second angle

The angle, \mathbf{-\dfrac{7 \cdot  \pi}{4}}, gives; tan \left(-\dfrac{7 \cdot \pi}{4} \right) = 1

The above value can be obtained as follows;

\mathbf{\dfrac{\dfrac{\sqrt{2} }{2} }{\dfrac{\sqrt{2} }{2} }}  = 1

Which gives;

  • -\dfrac{7 \cdot \pi}{4}  \Longleftrightarrow \left(\dfrac{\sqrt{2} }{2}, \, \dfrac{\sqrt{2} }{2} \right)

Third angle

The angle 210° gives; tan(210°) = \mathbf{\frac{1}{\sqrt{3} }}, which can be obtained as follows;

\sqrt{ \dfrac{1}{3} } = \mathbf{\dfrac{-\dfrac{1}{2} }{-\dfrac{\sqrt{3} }{2} }}

Therefore;

  • 210^{\circ} \Longleftrightarrow \left(-\dfrac{\sqrt{3} }{2}, \ -\dfrac{1}{2} \right)

Learn more about the unit circle here:

brainly.com/question/1673530

6 0
2 years ago
Which line is a linear model for the line?<br><br> 1. A<br> 2. B<br> 3. C<br> 4. D
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2 is the answer i beileve

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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