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atroni [7]
3 years ago
10

Solve using algebraic equation: 5sin2x=3cosx

Mathematics
2 answers:
disa [49]3 years ago
5 0
\bf 5sin(2x)=3cos(x)\qquad \qquad  sin(2\theta)=2sin(\theta)cos(\theta)\qquad thus
\\\\
5[2sin(x)cos(x)]=3cos(x)\implies 10sin(x)cos(x)=3cos(x)
\\\\
10sin(x)cos(x)-3cos(x)=0\impliedby \textit{taking common factor}
\\\\\\
cos(x)[10sin(x)-3]=0\implies 
\begin{cases}
cos(x)=0\to &\measuredangle x=cos^{-1}(0)
\\\\
sin(x)=\frac{3}{10}\to &\measuredangle x = sin^{-1}\left( \frac{3}{10} \right)
\end{cases}
Mila [183]3 years ago
4 0

Answer:

x = 17.46° or x = 90°

Step-by-step explanation:

We need to solve 5sin2x=3cosx

sin2x =

Substituting

5\times 2sinx cosx = 3 cosx\\\\cosx(10sinx-3)=0\\\\sinx=0.3\texttt{ or }cosx=0\\\\x=17.46^0\texttt{ or }x=90^0

x = 17.46° or x = 90°

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Complete the equivalent equation for –7x<span> – 60 = </span>x2<span> + 10</span>x.

(x<span> + 5</span>)(x<span> + 12) = 0</span>

What are the solutions of –7x<span> – 60 = </span>x2<span> + 10</span>x?

x<span> = -12 or -5</span>

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the range of this function is [-7, 2)   (Answer A)

Step-by-step explanation:

The "range" of this function is the list of all values that the function can take on according to the rule shown in the graph.  The smallest such value (the smallest y-value) is -7, obtained when x = -2. The largest is just less than 2; we know this because there is an empty circle at (1, 2) instead of a shaded circle.

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What is the measure of ZCED?
Vlad [161]

Answer:

The correct option is A.

A) m, because ΔABC ~ ΔEDC

Step-by-step explanation:

Consider the both triangles.

<B = 60°

<D = 60°

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