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Assoli18 [71]
3 years ago
10

Help I don’t understand this

Mathematics
1 answer:
Ganezh [65]3 years ago
5 0

Answer:

Step-by-step explanation:

they are opposite angles, so we put them equal to each other.

25.

6a+10= 130

6a=120    a=20   so now we plug it in 6(20) +10= 130

26.   4a-4=2a+30

      2a=34      a=17   sso now we plug in 4(17)-4= 64    2(17)+30= 64

27.    6y+1=4y+9                             2x-5=x+7

          2y=8                                      x=2

         y=4

now plug in 6(4)+1=25     4(4)+9=25     2(2)-5= -1     (2)+7=9

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Sin(x)^4+ cos(x)^4=1/2
posledela
I'll assume that what was meant was \sin ^4 x + \cos ^4 x = \dfrac{1}{2}.

The exponent in the funny place is just an abbreviation:   \sin ^4 x = (\sin x)^4.

I hope that's what you meant. Let me know if I'm wrong.

Let's start from the old saw

\cos^2 x + \sin ^2x = 1

Squaring both sides,

(\cos^2 x + \sin ^2x)^2 = 1^2

\cos^4 x + 2 \cos ^2 x \sin ^2x +\sin ^4x = 1

\cos^4 x + \sin ^4x = 1 - 2 \cos ^2 x \sin ^2x

So now the original question 

\sin ^4 x + \cos ^4 x = \dfrac{1}{2}

becomes
1 - 2 \cos ^2 x \sin ^2x = \dfrac{1}{2}

4 \cos ^2 x \sin ^2x = 1

Now we use the sine double angle formula

\sin 2x = 2 \sin x \cos x

We square it to see

\sin^2 2x = 4\sin^2 x \cos^2 x = 1

Taking the square root,

\sin 2x = \pm 1

Not sure how you want it; we'll do it in degrees. 

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine.  They're supplementary angles which add to 180^\circ.  But when the sine is 1 or -1 like it is here, we're looking at 90^\circ and -90^\circ, which are essentially their own supplements, slightly less messy. 

That means we have two equations:

\sin 2x = 1 = \sin 90^\circ

2x = 90^\circ + 360^\circ k \quad integer k

x = 45^\circ + 180^\circ k

or 


\sin 2x = -1 = \sin -90^\circ

2x = -90^\circ+ 360^\circ k

x = - 45^\circ + 180^\circ k

We can combine those for a final answer,

x = \pm 45^\circ + 180^\circ k \quad integer k

Check.  Let's just check one, how about

x=-45^\circ + 180^\circ = 135^\circ

\sin(135)= 1/\sqrt{2}

\sin ^4(135)=(1/\sqrt{2})^4 = 1/4

\cos ^4(135)=(-1/\sqrt{2})^4 = 1/4

\sin ^4(135^\circ) +\cos ^4(135^\circ) = 1/2 \quad\checkmark


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attashe74 [19]

Answer:

Can you type out the question? it is hard to read and the angle makes it harder

Step-by-step explanation:

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