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never [62]
3 years ago
6

CosA + cosB + cosC = 1 + 4sinA/2 sinB/2 sinC/2

Mathematics
1 answer:
bulgar [2K]3 years ago
6 0

\cos(A)  +  \cos( B )  +  \cos(C)  \\  = 2 \cos( \frac{A + B}{2} )  \cos( \frac{ A- B}{2} )  + 1 - 2 { \sin }^{2}  \frac{C}{2}  \\  = 1 + 2\cos( \frac{\pi - C}{2} )   \cos( \frac{A - B}{2} )  - 2 { \sin }^{2}  \frac{C}{2}  \\  = 1 + 2 \sin \frac{C}{2}  \cos( \frac{A - B}{2} )  - 2 { \sin }^{2}  \frac{C}{2}  \\  = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}]  \\  =  1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A  +  B}{2} )] \\  = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2}  +\frac{A  -  B}{2} }{2} )  \sin( \frac{ \frac{A + B}{2}   - \frac{A  -  B}{2} }{2} )  \\  = 1 + 4 \sin \frac{A}{2}  \sin \frac{B}{2}  \sin \frac{C}{2}

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Subtract. 5/9-(3 1/3) Enter your answer, as a mixed number in simplest form, in the box.
Vaselesa [24]

Answer:

-2\frac{7}{9}

Step-by-step explanation:

\frac{5}{9} - 3\frac{1}{3} = \frac{5}{9} - \frac{10}{3} = \frac{5}{9} - \frac{30}{9} = -\frac{25}{9} = -2\frac{7}{9}

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3 years ago
A group of volunteers made 21,736 sandwiches for a community service project. There are 143 volunteers in the group. On
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b

Step-by-step explanation:

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4 0
3 years ago
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Which graph shows a dilation?
dimulka [17.4K]

Answer:

The third one.

Explanation:

A dilation is a shrink or a stretch of a figure.  

In a dilation, all sides either increase or decrease by the same scale factor.  Additionally, in a dilation the angle measures of the figure do not change.

In the first figure, we can see that the base angles of the pre-image are slightly different than those of the image.  This is not a dilation.

In the second figure, the angles are noticeably different; again, not a dilation.

In the fourth figure, much like the second figure, the angles are noticeably different.  This is not a dilation.

In the third figure, however, we can see that the slanted sides of the larger figure go through three boxes; they are three units long.  Additionally we can see that the slanted sides of the smaller figure go through 1 side; this is a dilation b a factor of 3.  

The base sides of the third figure, in the larger shape, are 6 units long; in the smaller figure, they are 2 units long.  This is a dilation by a factor of 3.

6 0
3 years ago
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Paladinen [302]
The answer is the last one
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Money is borrowed at 9% simple interest after one year $1209.90 pays off the loan how much was originally borrowed
Kamila [148]

Answer:

10,881$

Step-by-step explanation:

time = 1 year

amount paid =  $1209.90

percent borrowed =  9%

therefore originally borrowed = $1209.90 X 9% X 1 year

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2 years ago
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