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3 years ago

What is the value of x in the equation 8+4 = 2(x-1)? 5 11 2 13 2. 07

Mathematics

1 answer:

earnstyle [38]3 years ago

3 0

Answer:

Step-by-step explanation:

8+4=2(x-1) (Given)

12=2x-2 (Distribute and simplify)

14=2x (Addition Property Of Equality)

7=x (Division Property Of Equality)

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The following equation involves a trigonometric equation in quadratic form. Solve the equation on the interval [0,2π).

Effectus [21]

Answer:

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}$

Step-by-step explanation:

Given the quadratic equation as:

$2sin^2x+sinx=1\\OR\\2sin^2x+sinx-1=0$

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Now, the equation becomes:

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$\Rightarrow 2y^2+2y-y-1=0\\\Rightarrow 2y(y+1)-1(y+1)=0\\\Rightarrow (2y-1)(y+1)=0\\\Rightarrow 2y-1 = 0, y+1 = 0\\\Rightarrow y = \dfrac{1}{2}, y = -1$

So, the solution to the given trigonometric quadratic equation is:

$sinx = \dfrac{1}{2}$

and

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$sin\theta$ can have a value equal to $\frac{1}{2}$ in 1st and 2nd quadrant.

So, $x$ can be

$30^\circ, 150^\circ\\OR\\\dfrac{\pi}{6}, \dfrac{5\pi}{6}$

For $sinx=-1$ ,

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So, the answer is:

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}$

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goldenfox [79]

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Step-by-step explanation:

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