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Fantom [35]
3 years ago
10

Find the products:

Mathematics
1 answer:
sesenic [268]3 years ago
4 0

Answer:

Step-by-step explanation:

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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
Half a number is at least 2 units from 20. write the sentence as an absolute value inequality
Anuta_ua [19.1K]

Answer:

|1/2x - 20| ≥ 2

Step-by-step explanation:

The number is half of two and at least two units away.

8 0
3 years ago
Read 2 more answers
Can someone please explain step by step on how I subtract fractions like for an a example!
kotykmax [81]

Keep the denominators the same and subtract the numerators. So for example in your example:

7/8 - 3/8

Leave the 8 alone. Subtract 3 from 7.

7 - 3 = 4

So answer is:

4/8

Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2

3 0
3 years ago
Read 2 more answers
If you share 7 apples equally with 3 people then there are 2 1/3. Frost complete the sentence. Then , briefly explain what the w
8090 [49]

Answer:

The whole number 2 is the number of whole apples each person gets.  The numerator 1 is the number of pieces of the remaining apple each person gets; the denominator 3 is the number of pieces the remaining apple is cut into.

8 0
2 years ago
6x + 14 = 20<br> Show your work <br> Solve the equation
DIA [1.3K]

Answer:

X = 1

Step-by-step explanation:

subtract 14 from both sides

6x = 6

divide both sides by 7

X = 1

5 0
2 years ago
Read 2 more answers
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