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skelet666 [1.2K]

7 months ago

11

Michael is constructing a circle circumscribed about a triangle. he has partially completed the construction. what should be his

next step in the construction?

1 answer:

earnstyle [38]7 months ago

6 0

Answer:

Connect the arcs to make a perpendicular bisector

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I need some help. Please

Ilya [14]

Are you able to ask your teacher?

7 0

2 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

Find the vertex of the given function.<br> f(x) = |x+1| -7

kenny6666 [7]

Answer:

(-1, -7)

Step-by-step explanation:

Used desmos, also, in these situations I believe you can take the number inside the brackets and make it negative and keep the number outside the same to find the vertex.

7 0

2 years ago

Read 2 more answers

Identify the terminal point for a 30° angle in a unit circle.

Afina-wow [57]

Answer:

The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).

Step-by-step explanation:

4 0

2 years ago

Hey guys, i would appreciate it if yall could help me out :)

exis [7]

Answer:

Equation should have an equal sign

Inequality should have the inequality sign

Expression has no signs

Step-by-step explanation:

8 0

2 years ago