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2 years ago

What does it mean for a differential equation to be autonomous?

1 answer:

7 0

The term "autonomous" refers to an ordinary differential equation that relates the derivatives of the dependent variable as a function *only* of the dependent variable. In other words, the ODE doesn't explicitly depend on the independent variable.

Examples:

$y'=y^2-1$ is autonomous

$y'=y^2-1+x$ is *not* autonomous

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All of the following are equivalent except<br> 7x2<br> 4x+3x<br> (4+3)x<br> 7x

swat32

Answer:

7x2

Step-by-step explanation:

7x2 is 14 and all the other ones equal 7

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2 years ago

Read 2 more answers

Each of the numbers 1 through 7 is written on a small piece of paper and placed in a box. What is the probability of picking a p

gregori [183]

Answer:

Either C or B I’m not quite sure which one. I’m sorry

Step-by-step explanation:

5 0

2 years ago

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Determine the domain and range of the function f(x)= 3x+2. Also, state the intervals where the function f(x)= 3x+ 2 is increasin

aev [14]

Answer:

Increasing on it's domain $(-\infty,\infty)$ because the slope is positive.

The domain and range are both all real numbers, also known as

$(-\infty,\infty)$ .

Step-by-step explanation:

All domain really means is what numbers can you plug in and you get number back from your function.

I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.

The domain is all real numbers.

In interval notation that is $(-\infty,\infty)$ .

Now the range is the set of numbers that get hit by y=3x+2.

Well y=3x+2 is a linear function that is increasing. I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.

If slope is positive, then the line is increasing.

If slope is negative, then the line is decreasing.

So y=3x+2 hits all values of y because it is increasing forever. The range is all real numbers. In interval notation that is $(-\infty,\infty)$ .

3 0

3 years ago

Nancy's morning routine involves getting dressed, eating breakfast, making her bed, and driving to work. Nancy spends ⅓ of the t

devlian [24]

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

8 0

2 years ago

The circumference of a circular field is 279.46 yards. What is the radius of the field? Use 3.14 for π and do not round your ans

wel

Answer:

44.5 yards

Step-by-step explanation:

Start with the formula of the circumference of a circle.

C = πd

Now all you have to do is plug in the numbers.

279.46 = (3.14)d

Divide both sides by 3.14

d = 89

But since you're finding the radius, you have to divide the diameter by 2.

89/2 = 44.5

6 0

2 years ago