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Harman [31]
3 years ago
10

What is the least number of solution a quadratic system can have

Mathematics
1 answer:
Setler79 [48]3 years ago
8 0
The least number of quadratic system can have is Two real solutions or no real solutions. 
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2sin^2 2x=2<br><br> In the domain [0,2pi)<br><br> What can x equal ( in radians).
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Bear in mind that, when it comes to trigonometric functions, the location of the exponent can be a bit misleading, however recall that sin²(θ) is really [ sin( θ )]²,


\bf 2sin^2(2x)=2\implies sin^2(2x)=\cfrac{2}{2}&#10;\\\\\\&#10;sin^2(2x)=1\implies [sin(2x)]^2=1\implies sin(2x)=\pm\sqrt{1}&#10;\\\\\\&#10;sin(2x)=\pm 1\implies sin^{-1}[sin(2x)]=sin^{-1}(\pm 1)

\bf \measuredangle 2x=sin^{-1}(\pm 1)\implies \measuredangle 2x=&#10;\begin{cases}&#10;\frac{\pi }{2}\\\\&#10;\frac{3\pi }{2}&#10;\end{cases}\\\\&#10;-------------------------------\\\\&#10;\measuredangle 2x=\cfrac{\pi }{2}\implies \measuredangle x=\cfrac{\pi }{4}\qquad \qquad \qquad \qquad \measuredangle 2x=\cfrac{3\pi }{2}\implies \measuredangle x=\cfrac{3\pi }{4}
3 0
3 years ago
Find x for,<br> sin⁻¹ 4x + sin⁻¹ 3x = -<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B2%7D" id="TexFormula1" title="\
Novay_Z [31]
<h2>Explanation:</h2><h2></h2>

Let's solve this problem graphically. Here we have the following equation:

sin^{-1}(4x) + sin^{-1}(3x) = -\frac{\pi}{2}

So we can rewrite this as:

f(x)=sin^{-1}(4x) + sin^{-1}(3x) \\ \\ g(x)= -\frac{\pi}{2}

So the solution to the equation is the x-value at which the functions f and g intersect. In other words:

f(x)=g(x) \\ \\ sin^{-1}(4x) + sin^{-1}(3x) = -\frac{\pi}{2}

Using graphing calculator, we get that this value occurs at:

\boxed{x=-0.2}

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3 years ago
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Answer:

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Step-by-step explanation:

15 divided by 16 equals .9375 so 2 15/16 is 2.9375

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qwelly [4]

Answer:

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Step-by-step explanation:

I hope this helps!

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