What is –12x–9=–6y in standard form?

Solve using algebraic equation: <br> 5sin2x=3cosx<br><br> (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .

6 0

3 years ago

15.3+x=1.3-x so how do I solve it

anzhelika [568]

Answer:

-7

Step-by-step explanation:

Let's try getting rid of the numbers to isolate the x.

Add x on both sides to get rid of the x on the right side and to get 2x on the left side. This leaves us with 15.3 + 2x = 1.3

Subtract 15.3 on both sides to get rid of the 15.3 on the left side.

This would leave us with 2x = -14

Divide 2 on both sides to isolate the x.

The answer is x = -7

3 0

3 years ago

Read 2 more answers

A survey was administered to high school seniors in Anytown. According to the survey results, fewer than 0.5% of the students dr

Feliz [49]

Answer: high test-retest reliability

Step-by-step explanation: this is because the result of the survey was thesame with the previous result, despite the space of time between when the first survey was conducted and when the second survey was conducted. There was know observable difference in result and if conducted in the next 3 months again, it will give same result, this strongly indicate that the survey has high test-retest reliability.

8 0

2 years ago

Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of

Nookie1986 [14]

Joel spent 72.5% of his time exercising after playing soccer on Tuesda

<h3>How to determine the percentage?</h3>

The given parameters are

Minutes spent on Tuesday = 27 more minutes than Monday

Total minutes spend = 60

This means that

Tuesday = Monday + 27

Monday + Tuesday = 60

Make Monday the subject in Tuesday = Monday + 27

Monday = Tuesday - 27

Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60

Tuesday - 27 + Tuesday = 60

Evaluate

2 * Tuesday = 87

Divide by 2

Tuesday = 43.5

The percentage of time spent exercising on Tuesday is then calculated as

Percentage = 43.5/60 * 100%

Evaluate the expression

Percentage = 72.5%

Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday