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prisoha [69]
3 years ago
5

3 Prove thatcos130°+cos 110+ cos10=0​

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
5 0

We know, cos A + cos B = 2cos(C+D)/2 × cos(C - D)/2

So,

cos 130 + cos 110 + cos 10

cos 130 + 2cos (110+10)/2 × cos( 110-10)/2

cos 130 + 2cos 60 × cos 50

cos ( 180 - 50 ) + 2cos60 cos 50

We know, cos ( 180 - A ) = -cos A

2cos 60 cos 50 - cos 50

Also, cos 60 = 0.5

2×0.5 cos 50 - cos50

cos 50 - cos 50

0  = RHS.

Hence proved

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Gabby received change worth $2.10. She received 3 more dimes than nickels and 4 less quarters than nickels. How many of each kin
xz_007 [3.2K]

Answer:

Gabby received

7 nickels

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3 quarters

Step-by-step explanation:

Let

x----> the number of dimes

y----> the number of nickels

z---> the number of quarters

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1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 ------> equation A

x=y+3-----> equation B

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substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

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therefore

Gabby received

7 nickels

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