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Naily [24]
2 years ago
8

Suppose a triangle has two sides of length 32 and 35, and that the angle

Mathematics
1 answer:
pantera1 [17]2 years ago
3 0

Answer:

The third side is around 58.043

Step-by-step explanation:

Use the law of cosines:  c^2=a^2+b^2-2abcos(C)

Plug in the two sides we know (into a and b) and the angle we know (into angle C).

Thus:

c^2=32^2+35^2-2(32)(35)cos(120)

Use a calculator:

c^2=3369\\

c=58.043087...

(Note: Make sure you're in Degrees mode.)

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the sum of the first six terms of a geometric series is 21/16 . if the common ratio is -1/2 , what is the first term?
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Answer:

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Step-by-step explanation:

The formula for the nth term of a geometric progression is

Un = ar^n- 1

The sum of the first six terms of a geometric series (U6) = 21/16

Common ratio = -1/2 ,

a = First term ??

21/16 = a × (-1/2 )^6- 1

21/16 = a ×(-2^-1)^5

21/16 = a × -2^-6

Cross Multiply

16 × a × -2^-6 = 21

a = 21/16 × -2^-6

a = 21/16 ×- 1/2⁶

a = 21/16 × -1/64

a = 21 ÷(-1/4)

a = 21 × -4

a = -84

The first term = 84

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Simplify by combining like terms: 9x - 3y -5x + 2y -x + 2
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Step-by-step explanation:

9x-5x-x-3y+2y=-2

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