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Helen [10]
3 years ago
15

A quantity with an initial value of 980 decays exponentially at a rate of 1% every 2

Mathematics
1 answer:
Firdavs [7]3 years ago
4 0

Answer:

821.94

Step-by-step explanation:

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2​
Oxana [17]

Answer:

The correct prove will be:

sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14}) = \frac{1}{8}

Step-by-step explanation:

    sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})

            Multiply and Divide by 2cos(\frac{\pi }{14})

= \frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}

⇒ Let \frac{\pi }{14} = Ф  and 7Ф = \frac{\pi }{2}

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ               ∵cos7Ф = 0      

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ                              

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ      ∵sin7Ф = 1  

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14}) = \frac{1}{8}

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

#learnwithBrainly

4 0
3 years ago
7x – 4 = 5x - x + 35 whats the value of x?​
aksik [14]

Answer: x=15

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Given that f(x) = x² +8x+3 and g(x) = -x-7, which of the following is true?
Valentin [98]
B and C make sense to me.
4 0
2 years ago
|-6+8| = simplify the expression
lilavasa [31]

Answer:

2

Step-by-step explanation:

|-6+8|

Add/subtract the numbers: -6 + 8 = 2

= |2|

Apply the absolute value rule: |a| = a, a ≥ 0

= 2

8 0
3 years ago
A company sells boxes of small blue pom-poms (b) for $42 and boxes of large orange pom-poms (p) for $52. They make batches of sm
Strike441 [17]

Answer:

b = 40 - p

42b + 52p = 350

Step-by-step explanation:

Given : No. of small blue pom-pom boxes = b

            No. of large orange pom-poms    = p

           cost of 1 box of blue pom pom = $42

           cost of one  large orange pom-pom box = $52

Solution:

Since we are given that the company has only 40 boxes

⇒b+p=40

⇒b=40-p

Since cost of 1 box of blue pom pom = $42

So, cost of b box of blue pom pom = $42b

Since,cost of one  large orange pom-pom box = $52

So,cost of p  large orange pom-pom box = $52p

We are also given that the company plan to make $350

⇒42b+52p=350

Hence Option b is correct

b = 40 - p

42b + 52p = 350

4 0
3 years ago
Read 2 more answers
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