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Mamont248 [21]
4 years ago
9

Solve the following equation exactly on the interval 0 ≤ θ ≤ 2π ? cos 2θ + sin θ = 0

Mathematics
1 answer:
Ilya [14]4 years ago
7 0
\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------

\bf cos(2\theta )+sin(\theta )=0\implies 1-2sin^2(\theta )+sin(\theta )=0
\\\\\\
0=2sin^2(\theta )-sin(\theta )-1\implies 0=[2sin(\theta )+1][sin(\theta )-1]\\\\
-------------------------------\\\\
0=2sin(\theta )+1\implies -1=2sin(\theta )\implies -\cfrac{1}{2}=sin(\theta )
\\\\\\
\measuredangle \theta =
\begin{cases}
\frac{7\pi }{6}\\\\
\frac{11\pi }{6}
\end{cases}\\\\
-------------------------------\\\\
0=sin(\theta )-1\implies 1=sin(\theta )\implies \measuredangle \theta =\frac{\pi }{2}
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Step-by-step explanation:

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x = 9

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Step-by-step explanation:

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4 years ago
Box со
Levart [38]

Answer:

The man has 6 GHc20.00 notes and 4 GHc10.00 left

Step-by-step explanation:

Given

Amount = 3 GH¢50.00, 7  GH¢20.00 and 5 GH¢10.00

Spendings = GH¢80,00

Required

Determine how many GH¢20.00 and  GH¢10.00 notes left

The amount he has can be represented as:

Amount = 3 * GHc50.00 + 7 * GHc20.00 + 5 * GHc10.00

Spendings = GHc80.00

This can be represented as:

Spendings = GHc50.00+GHc20.00+GHc10.00

Represent:

GHc50.00 with x, GHc20.00 with y and GHc10.00 with z

So, we have:

Amount = 3 * GHc50.00 + 7 * GHc20.00 + 5 * GHc10.00

Amount = 3 *x + 7*y + 5*z

Amount = 3x + 7y + 5z

Spendings = GHc50.00+GHc20.00+GHc10.00

Spendings =x+y+z

Subtract the spendings from the total to get amount left

Amount\ Left= 3x + 7y +5z - (x+y+z)

Amount\ Left= 3x + 7y +5z - x-y-z

Collect Like Terms

Amount\ Left= 3x-x + 7y-y +5z-z

Amount\ Left= 2x + 6y +4z

Recall that, we have represented:

GHc50.00 with x, GHc20.00 with y and GHc10.00 with z

<em>This means that, the man has 6 GHc20.00 notes and 4 GHc10.00 left</em>

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3 years ago
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