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crimeas [40]
3 years ago
9

Write the product as a sum. 9cos(6x) cos(9x)

Mathematics
1 answer:
lys-0071 [83]3 years ago
3 0

Answer:

9/2 [ cos(15x) + cos(3x) ]

Step-by-step explanation:

9cos(6x) . cos(9x) can be expressed as

= 9/2 * 2cos (6x) * cos(9x)  next  here we will apply the rule

2cosA . cosB = cos(A+B)  + cos( A-B)

where A = 6x , B = 9x

hence : 9cos(6x) . cos(9x)  expressed as a sum will be

= 9/2 * [cos( 6x+ 9x) + cos( 6x - 9x ) ]

= 9/2 [ cos (15x ) + cos(-3x) ]

the final sum = 9/2 [ cos(15x) + cos(3x) ]

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N² + 14 = 12n<br>how do I solve by quadratic formula ​
inysia [295]

Answer:

n = 6 + \sqrt{22}  or  n = 6 - \sqrt{22}

Step-by-step explanation:

We can solve this equation using the quadratic formula OR Completing the Square method.

n² + 14 = 12n

rearrange :  n² - 12n + 14  = 0  

here  a= 1 , b = -12,  c = 14

the quadratic formula says:   x =  - b/ (2a)  +  root(b^2 - 4ac) / (2a)

or  x =  - b/ (2a)  -  root(b^2 - 4ac) / (2a)

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so   x =6 + \sqrt{22}   or  x = 6 - \sqrt{22}

In this case  x = n

n = 6 + \sqrt{22}  or  n = 6 - \sqrt{22}

3 0
3 years ago
Read 2 more answers
Do you agree with the researchers method of predicting the population? Why or why not?
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Step-by-step explanation:

Step 1:

If we substitute the values of n in the researcher's equation and we get the right values of a_{n}, we can agree with the researcher's method.

The researcher's formula is a_{n} = 1000(2)^{n-1}. Here a_{n} is the wombat population and n is the number of years.

Step 2:

When n = 1, a_{1} = 1000(2)^{1-1} =  1000(1) = 1,000,

when n = 2, a_{2} = 1000(2)^{2-1} = 1000(2) = 2,000,

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when n = 5, a_{5} = 1000(2)^{5-1} = 1000(16) = 16,000.

As all the values correspond to the values on the table, I agree with the researcher's method.

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