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3 years ago

The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?

Mathematics

1 answer:

stiv31 [10]3 years ago

3 0

Answer:

Step-by-step explanation:

1. Set up a equation.

2. X is the first, so the ones after x are x+2, x+4, x+6, x+8, and x+10.

3. That means that x+x+2+x+4+x+6+x+8+x+10=204.

4. Simplify. You would get that 6x+30=204.

5. Solve for x. 6x=174, so x=29.

6. Get the fourth number in the sequence. 29+6=35.

Answer: The fourth number in this sequence is 35.

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Answer:

$sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}$

Step-by-step explanation:

step 1

Find the $sin(\theta)$

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Remember that

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Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

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step 2

Find the sec(β)

Applying the trigonometric identity

$tan^2(\beta)+1= sec^2(\beta)$

we have

$tan(\beta)=\frac{4}{3}$

substitute

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Remember that

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therefore

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step 3

Find the sin(β)

we know that

$tan(\beta)=\frac{sin(\beta)}{cos(\beta)}$

we have

$tan(\beta)=\frac{4}{3}$

$cos(\beta)=\frac{3}{5}$

substitute

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step 4

Find sin(θ+β)

we know that

$sin(A + B) = sin A cos B + cos A sin B$

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$sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)$

we have

$sin(\theta)=-\frac{\sqrt{7}}{3}$

$cos(\theta)=-\frac{\sqrt{2}}{3}$

$sin(\beta)=\frac{4}{5}$

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substitute the given values in the formula

$sin(\theta + \beta) = (-\frac{\sqrt{7}}{3})(\frac{3}{5})+ (-\frac{\sqrt{2}}{3})(\frac{4}{5})$

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The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?​

The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?