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lys-0071 [83]
3 years ago
15

Please solve the eqution Cos4x + cos2x - 2 =0

Mathematics
1 answer:
horrorfan [7]3 years ago
6 0

cos4x = cos2x

We know that:

cos2x = 1-2cos^2 x

==> cos4x = 1-2cos^2 (2x)

Now substitute:

==> 1-2cos^2 (2x) = cos2x

==> 2cos^2 (2x) + cos2x - 1 = 0

Now factor:

==> (2cos2x -1)(cos2x + 1) = 0

==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3

==> x1= pi/6 , 7pi/6

==> x1= pi/6 + 2npi

==> x2= 7pi/6 + 2npi

==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.

<span>==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}</span>

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mr_godi [17]

We determine line m as follows:

*First, by theorem we have the following:

m_1=-\frac{1}{m_2}

Here m1 & m2 are the slopes of two perpendicular lines. For all lines that are perpendicular that is true, so we calculate the slope of line m using the slope of the function given [Which has a slope of 7/4]:

m_1=-\frac{1}{\frac{7}{4}}\Rightarrow m_1=-\frac{4}{7}

So, the slope of line m is -4/7. Now, using this slope and the point (-1, 4) we replace in the following expression:

y-y_1=m_1(x-x_1)

Here x1, y1 & m1 are the x-component of the point, the y-component of the point, and the slope of the line respectively, so we replace and solve for y:

y-4=-\frac{4}{7}(x-(-1))\Rightarrow y-4=-\frac{4}{7}x-\frac{4}{7}\Rightarrow y=-\frac{4}{7}x+\frac{24}{7}

And that last function of y is the line m.

8 0
1 year ago
Choose the lowest common denominator.
Brilliant_brown [7]

1) 8

2) -\frac{3}{4}=-\frac{6}{8}, so it is equal to -\frac{6}{8}+\frac{5}{8}

3) 1/8

4 0
2 years ago
The graph of a proportional relationship passes through (9, 18) and (1, y). Find y.
spayn [35]

Answer:

2

Step-by-step explanation:

Because it's a proportional relationship and it goes through the point (9, 18) the equation is y = 2x so when x = 1, y = 2.

8 0
3 years ago
What is the value of x + 186 when x = -21
fredd [130]

Answer:

165

Step-by-step explanation:

-21+186=165 .....

7 0
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stiv31 [10]

Answer:

9. No

10. Yes

Step-by-step explanation:

The first one is not, since you have (3, 3) and (3, 9).  In a function, each x maps to a single y.

The second one is since every x appears only once.

8 0
2 years ago
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