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3 years ago

What is the next three terms to a sequence -1/3125, 1/625, -1/125, 1/25

Mathematics

1 answer:

Natali [406]3 years ago

3 0

Answer:

-1/3125, 1/625, -1/125, 1/25 , -(1÷5) , 1 , -5

Step-by-step explanation:

1÷625÷(-1÷3 125) = -5

-1÷125÷(1÷625) = -5

(1÷25)÷(-1÷125) = -5

Then the common ratio of the geometric sequence is -5 then we keep multiplying by -5 each time to get the next term:

(1÷25)×(-5) = -(1÷5)

-(1÷5)×(-5) = 1

(1)×(-5) = -5

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2 years ago

Solve the following triangle. Given A=51 degrees b=40 c=45

STALIN [3.7K]

Answer:

$a=36.87\ units$

$B=57.47^o$

$C=71.53^o$

Step-by-step explanation:

step 1

Find the length side a

Applying the law of cosines

$a^2=b^2+c^2-2(b)(c)cos(A)$

substitute the given values

$a^2=40^2+45^2-2(40)(45)cos(51^o)$

$a^2=1,359.4466$

$a=36.87\ units$

step 2

Find the measure of angle B

Applying the law of sines

$\frac{a}{sin(A)} =\frac{b}{sin(B)}$

substitute the given values

$\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}$

$sin(B)=\frac{sin(51^o)}{36.87}{40}$

$B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o$

step 3

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$A+B+C=180^o$

substitute the given values

$51^o+57.47^o+C=180^o$

$108.47^o+C=180^o$

$C=180^o-108.47^o=71.53^o$

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3 years ago