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andrew-mc [135]

2 years ago

7

PLEASE HELP! 8 POINTS!! Find the value

1 answer:

Pepsi [2]2 years ago

5 0

Answer:

-sqrt(3)/2

Step-by-step explanation:

Use double angle identity for sin(2x)

sin(2x)=2sin(x)cos(x)

We are given sin(x)=-1/2 so we already have so far that:

sin(2x)=2(-1/2)cos(x)

sin(2x)=-1*cos(x)

We just need to find cos(x).

x is in the fourth quadrant so cosine will be positive there

knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.

So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2

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Lines k and n intersect on the y-axis

avanturin [10]

a) The equation of line k is:

$y = -\frac{202}{167}x + \frac{598}{167}$

b) The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

The equation of a line, in <u>slope-intercept formula</u>, is given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change.
b is the y-intercept, which is the value of y when x = 0.

Item a:

Line k intersects line m with an angle of 109º, thus:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

In which $m_1$ and $m_2$ are the slopes of <u>k and m.</u>

Line k goes through points (-3,-1) and (5,2), thus, it's slope is:

$m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}$

The tangent of 109 degrees is $\tan{109^{\circ}} = -\frac{29}{10}$
Thus, the slope of line m is found solving the following equation:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

$-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}$

$m_2 - \frac{3}{8} = -\frac{29}{10} - \frac{87}{80}m_2$

$m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}$

$\frac{167m_2}{80} = \frac{-202}{80}$

$m_2 = -\frac{202}{167}$

Thus:

$y = -\frac{202}{167}x + b$

It goes through point (-2,6), that is, when $x = -2, y = 6$ , and this is used to find b.

$y = -\frac{202}{167}x + b$

$6 = -\frac{202}{167}(-2) + b$

$b = 6 - \frac{404}{167}$

$b = \frac{6(167)-404}{167}$

$b = \frac{598}{167}$

Thus. the equation of line k, in slope-intercept formula, is:

$y = -\frac{202}{167}x + \frac{598}{167}$

Item b:

Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

$-\frac{202}{167}m = -1$

$m = \frac{167}{202}$

Then

$y = \frac{167}{202}x + b$

Also goes through point (-2,6), thus:

$6 = \frac{167}{202}(-2) + b$

$b = \frac{(2)167 + 202(6)}{202}$

$b = \frac{1546}{202}$

The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

A similar problem is given at brainly.com/question/16302622

7 0

2 years ago

Sole for y<br> k = p/2(y+w)<br> y =

mojhsa [17]

Answer:

<u>Answer</u><u>:</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>(</u><u>2</u><u>k</u><u> </u><u>-</u><u>pw</u><u>)</u><u>/</u><u>p</u>

Step-by-step explanation:

$k = \frac{p}{2} (y + w)$

multiply 2 on both sides:

$k \times 2 = 2 \times \frac{p}{2} (y + w) \\ \\ 2k = p(y + w)$

open the bracket:

$2k = py + pw$

subtract pw from both sides:

$2k - pw = (py + pw) - pw \\ 2k - pw = py$

divide p on both sides:

$\frac{2k - pw}{p} = \frac{py}{p} \\ \\ y = \frac{2k - pw}{p}$

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Sergio [31]

Since he completes 10 minutes each day for five days, he completes 50 minutes.

The percentage of his total requirement would be 50/100 = 0.5 = 50%.

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Zepler [3.9K]

Answer=18
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What number should be added to both sides of the equation to complete the square? x^2-40x=0

mylen [45]

Answer:

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Step-by-step explanation:

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