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MaRussiya [10]
3 years ago
11

Verify the identity sin^2(x)cos^2(x)=1/8(1-cos(4x))

Mathematics
1 answer:
bixtya [17]3 years ago
5 0

cos^2(x) = 1/2 + (1/2)cos(2x)

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

sin^2(x)cos^2(x)

= [1/2 - (1/2)cos(2x)][1/2 + (1/2)cos(2x)]

(a - b)(a + b) = a^2 - b^2

= (1/2)^2 - (1/2)^2[cos^2(2x)]

= 1/4 - (1/4)cos^2(2x)

= (1/4)[1 - cos^2(2x)]

= (1/4)[sin^2(2x)]

= (1/4)[1/2 - (1/2)cos(4x)]

= (1/4)(1/2)[1 - cos(4x)]

= (1/8)[1 - cos(4x)]

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Lemur [1.5K]

Answer:

V = 408    SA = 378

Step-by-step explanation:

To find the volume, you need to first find out the area and multiply it by overall length.

A = 1/2 (6)(8)

= 24

Volume = 24 x 17

= 408

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SA = Front and Back + Right Side + Left Side + Bottom

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6 0
3 years ago
Ten sixth-grade students in five different countries—United States, Australia, South Africa, Canada, and New Zealand—were asked
Crank

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12.3.5.5 or  New Zealand is a mean. or MAD means not now what you want to say,

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6 0
3 years ago
Does anyone know how to do this ??? <br> -view attachment
cricket20 [7]

As soon as I read this, the words "law of cosines" popped
into my head.  I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.

The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.

To find angle-B, the law of cosines says

       b² = a² + c² - 2 a c cosine(B)

B  =  angle-B
b  =  the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9

                  (1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)

                 1.96  =  (1) + (3.61)  -  (3.8) cos(B)

Add  3.8 cos(B)  from each side:

                 1.96 + 3.8 cos(B) = 4.61

Subtract  1.96  from each side:

                             3.8 cos(B) =  2.65

Divide each side by  3.8 :

                                  cos(B)  =  0.69737  (rounded)

Whipping out the
trusty calculator:
                                 B  = the angle whose cosine is 0.69737

                                      =  45.784° .

Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...

By gosh !  Choice 'B' is  45.8° !                    yay !
I'll bet that's it !

8 0
4 years ago
How do you do this? It's identifying are and perimeter
nikklg [1K]
You add up all the sides

5 0
4 years ago
Read 2 more answers
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