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3 years ago

Use chain rule to show that d(4cos2x)/dx=-8sin2x

1 answer:

4 0

$\dfrac{\mathrm d(4\cos2x)}{\mathrm dx}=4\dfrac{\mathrm d(\cos2x)}{\mathrm dx}=-4\sin2x\dfrac{\mathrm d(2x)}{\mathrm dx}=-8\sin2x$

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Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the following

bazaltina [42]

Answer:

16 years.

Step-by-step explanation:

Please consider the complete question.

Assume that the suburb has a population of 686,000 and is growing at a rate of 4000 per year. Assume that the city has a population of 942,000 and is declining at a rate of 12000 per year. In how many years will the populations of the suburb and the city be equal?

Let x represent number of years.

Growth function would be $G(x)=4000x+686,000$ and decline function would be $D(x)=942,000-12,000x$ .

To find the time when both populations will be equal, we will equate both functions as:

$4000x+686,000=942,000-12,000x$

$4000x+12,000x+686,000=942,000$

$16,000x+686,000=942,000$

$16,000x=942,000-686,000$

$16,000x=256,000$

$\frac{16,000x}{16,000}=\frac{256,000}{16,000}$

$x=16$

Therefore, in 16 years the populations of the suburb and the city will be equal.

6 0

3 years ago

Ms.Gartland bought x number of shirts for the new members of her chorus.The cost for x number of shirts,including $3.99 shipping

lorasvet [3.4K]

77.49 - 3.99 = $73.5

73.5 / 12.25 = 6 Shirts

6 0

3 years ago

Read 2 more answers

Select the correct answer.

tiny-mole [99]

Answer:

5 more than the absolute value of the cube of a number

4 0

3 years ago

the terms in sequence A increases by 3. The terms in sequence B increase by 8. In which sequence do the terms form a steeper lin

il63 [147K]

Solution: The sequence B shows the steeper line.

Exanation:

The line having greater slope is always steeper than the other lines.

Since it is given that the sequence A increases by 3 and the sequence B increases by 8. It means for each additional value the sequences increased by 3 and 5 units respectively.

The slope of line is rate of change of one variable with respect to another variable.

The sequence A increased by 3, therefore the slope of line of sequence A is 3.

The sequence B increased by 8, therefore the slope of line of sequence B is 8.

Since the slope of sequence B is greater than the slope of sequence A, therefore the line of sequence B is steeper than the line of sequence A.

The sequence A can be defined as 3,6,9,12,.... and the sequence B can be defined as 8,16,24,....

So the coordinates points of sequence A are (0,0)(1,3),(2,6) and the coordinates points of sequence B are (0,0),(1,8),(2,16).

From the given figure it is notes that the blue line is steeper than red line.

Therefore, the sequence B shows the steeper line.

6 0

4 years ago

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Nicole used 3\8 of her ribbion to wrap a present.. If she used 6feet of ribbion for the present, how much ribbion did Nicole hav

Karolina [17]

That would be 16 feet of ribbon.

5 0

3 years ago

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