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2 years ago

Thanks if you help me

Mathematics

2 answers:

BabaBlast [244]2 years ago

7 0

A=(4.5,1)
B=(0,6)
C=(9,3)

USPshnik [31]2 years ago

6 0

Answer:

A= (1,5)

B=(0,6)

C=(3,9)

Step-by-step explanation:

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Square root of 2tanxcosx-tanx=0

kobusy [5.1K]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3242555

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Solve the trigonometric equation:

$\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}$

Restriction for the solution:

$\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.$

Square both sides of (i):

$\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}$

$\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}$

Let

$\mathsf{sin\,x=t\qquad (0\le t$

So the equation becomes

$\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}$

Solving the quadratic equation:

$\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.$

$\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}$

$\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}$

You can discard the negative value for t. So the solution for (ii) is

$\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}$

Substitute back for t = sin x. Remember the restriction for x:

$\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}$

where k is an integer.

I hope this helps. =)

3 0

2 years ago

Factor out the greatest common factor from the following polynomial.

Ulleksa [173]

Answer:

i pretty sure its 6

Step-by-step explanation:

i did the research

4 0

1 year ago

Read 2 more answers

Sandy mixed together 9 gallons of one brand of juice and 8 gallons of a second brand of juice, which contains 48 percent real fr

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Answer:

14 % pure juice comes from first brand

Step-by-step explanation:

Mixture:

17 gal 30% contains: 17x 30% = 5.10 gal pure juice

Second brand:

8 gal 48% contains: 8x40% = 3.84 gal pure juice

5.10 − 3.84 = 1.26 gal

1.26 gal is coming from 9 gal of first brand

The percentage of first brand is:

(1.26/9) x100 = 14 % pure juice.

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2 years ago

The functions f(x) and g(x) are shown on the graph.

Grace [21]

Answer:

I believe the answer is D.

6 0

2 years ago

On a test that has a normal distribution, a score of 49 falls two standard deviations below the mean, and a score of 61 falls on

Zolol [24]

The mean of this test will be 57.

<h3>What is Standard Deviation and Mean?</h3>

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

The mean can be used to get an overall idea, or picture, of the data set.

Let Mean be 'm'

and standard deviation= $\sigma$

So, m-2 $\sigma$ =49

and, m + $\sigma$ =61

Solving the above two equation we get

$\sigma =4$

Now, m= 61- $\sigma$

= 61-4

= 57

So , the mean of this test will be =57

Learn more about mean and standard deviation here:

brainly.com/question/16030790

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6 0

1 year ago