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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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You bought a new car in 2015 for $32,000 that is depreciating in value by 15% each year. Write a function to represent this situ
Hitman42 [59]

Function: x = years

x = $32,000-15%x

Value of car in 2020:

$8000

4 0
2 years ago
Which logarithmic equation is equivalent to the exponential equation below? E^a=35
oee [108]

Answer:

a = ln 35

Step-by-step explanation:

Given e^a = 35, take the natural log of both sides, obtaining:

ln e^a = ln 35. Recall that ln e^x = x, which means that ln e^a = a.

Then a = ln 35.

Next time, please share the answer choices!

7 0
3 years ago
Read 2 more answers
1/2b+9/4=7/4 solve the equation
AlladinOne [14]
First subtract 9/4 from each side

1/2b=-2/4

Simplify the 2/4

1/2b=-1/2

Divide each side by 1/2

b = -1
4 0
3 years ago
-5/4x - 2)=-2(3 +6x)
Alex

Answer:

x = (-16)/43

Step-by-step explanation:

Solve for x:

(-5 x)/4 - 2 = -2 (6 x + 3)

Put each term in (-5 x)/4 - 2 over the common denominator 4: (-5 x)/4 - 2 = (-5 x)/4 - 8/4:

(-5 x)/4 - 8/4 = -2 (6 x + 3)

(-5 x)/4 - 8/4 = (-5 x - 8)/4:

(-5 x - 8)/4 = -2 (6 x + 3)

Multiply both sides by 4:

(4 (-5 x - 8))/4 = -2×4 (6 x + 3)

(4 (-5 x - 8))/4 = 4/4×(-5 x - 8) = -5 x - 8:

-5 x - 8 = -2×4 (6 x + 3)

4 (-2) = -8:

-5 x - 8 = -8 (6 x + 3)

Expand out terms of the right hand side:

-5 x - 8 = -48 x - 24

Add 48 x to both sides:

48 x - 5 x - 8 = (48 x - 48 x) - 24

48 x - 48 x = 0:

48 x - 5 x - 8 = -24

48 x - 5 x = 43 x:

43 x - 8 = -24

Add 8 to both sides:

43 x + (8 - 8) = 8 - 24

8 - 8 = 0:

43 x = 8 - 24

8 - 24 = -16:

43 x = -16

Divide both sides of 43 x = -16 by 43:

(43 x)/43 = (-16)/43

43/43 = 1:

Answer:  x = (-16)/43

8 0
3 years ago
Approximately 52% of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls
Leni [432]

Answer:

Option A is right

Step-by-step explanation:

Given that approximately 52% of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls. The most likely explanation for the difference between the observed results and the expected results in this case is

A) variability due to sampling

-- True because there is a slight difference whichmay be due to sampling fluctuations.

B) bias

False because given that 100 random births selected

C) nonsampling error

False.  There is no chance for systematic error here.

d) Confounding:  There is no confounding variable present inchild birth since each is independent of the other

e) a sampling frame that is incomplete

False because the sampling is done correctly.

8 0
3 years ago
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