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stira [4]
3 years ago
12

D/dx(sin x/2+cos x) = (a + b cos x)/(2+cos x)^2 find a and b.​

Mathematics
1 answer:
Talja [164]3 years ago
7 0

Answer:

a = 1 and b = 2

Step-by-step explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

=   [(2 + cos x) * cosx -  sin x * - sin x)]  /  (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) /  (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 +  2 cos x)  /   (2 + cos x)^2

- so a = 1 and b = 2.

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1 year ago
1. Given the below sequence: -1, -3, -5, -7, . . . (a) What are the next 3 terms? (b) Is this an arithmetic or geometric sequenc
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(a) -7 , - 9 , - 11

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(c) There is a common difference of -2

(d) -53

Step-by-step explanation:

(a) To find the next three terms , we must firs check if it is arithmetic sequence or a geometric sequence . For it to be an arithmetic sequence , there must be a common difference :

check :

-3 - (-1) = -5 - (-3) = -7 - (-5)  = -2

This means that there is a common difference of -2 , which means it is an arithmetic sequence.

The next 3 terms we are to find are: 5th term , 6th term and 7th term.

t_{5} = a + 4d

t_{5} = - 1 + 4 ( -2 )

t_{5} = -1 - 8

t_{5} = - 9

6th term = a +5d

t_{6} = -1 + 5(-2)

t_{6} = -1 - 10

t_{6} = - 11

t_{7} = a + 6d

t_{7} = -1 + 6 (-2)

t_{7} = -1 - 12

t_{7} = -13

Therefore : the next 3 terms are : -9 , -11 , - 13

(b) it is an arithmetic sequence because there is a common difference which is -2

(c) Because of the existence of common difference

(d) t_{27} = a + 26d

t_{27} = -1 + 26 ( -2 )

t_{27} = -1 - 52

t_{27} = - 53

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3 years ago
HELP ME ASAP PLEASE?!?<br> Find the length of the missing side. Simplify all radicals.
Anuta_ua [19.1K]
The missing side would be 10
7 0
3 years ago
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