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2 years ago

Function f(x) represents the population of bacteria x hours after 9 a.m. What does f(2)-f(1) represent?

Mathematics

1 answer:

Kitty [74]2 years ago

4 0

x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)

f(x) = population count x hours after 9 am

f(1) = population count at 10 am (1 hour later)

f(2) = population count at 11 am (2 hrs after 9 am)

f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.

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Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

Mama L [17]

Multiplying both sides by $y^2$ gives

$xy^2\dfrac{\mathrm dy}{\mathrm dx}+y^3=1$

so that substituting $v=y^3$ and hence $\frac{\mathrm dv}{\mathrm dv}=3y^2\frac{\mathrm dy}{\mathrm dx}$ gives the linear ODE,

$\dfrac x3\dfrac{\mathrm dv}{\mathrm dx}+v=1$

Now multiply both sides by $3x^2$ to get

$x^3\dfrac{\mathrm dv}{\mathrm dx}+3x^2v=3x^2$

so that the left side condenses into the derivative of a product.

$\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2$

Integrate both sides, then solve for $v$ , then for $y$ :

$x^3v=\displaystyle\int3x^2\,\mathrm dx$

$x^3v=x^3+C$

$v=1+\dfrac C{x^3}$

$y^3=1+\dfrac C{x^3}$

$\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}$

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2 years ago

Which scenario can the following graph describe? A)the total time a kite is up in the air as it goes up for a little bit ,comes

Vadim26 [7]

Answer:

Option C is the correct answer.

Step-by-step explanation:

We are given,

A graph where the function first increases and then decreases to touch the x-axis and the increases.

It is required to find the corresponding situations.

So, from the options we have that,

The graph represents the speed of a vehicle which first increases (as it accelerates), then decreases (slows down) and then touch the x-axis (stops at the light) and then increases (accelerates on the ramp for a freeway).

Hence, option C is scenario that the graph describes.

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2 years ago

during a Major League playoff series there was 43242 people in attendance at the first game and 44106 people in the attendance o

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There were 87,348 people who attended the games.

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2 years ago

Ab-0.5bab−0.5ba, b, minus, 0, point, 5, b when a=1a=1a, equals, 1 and b=5b=5b, equals, 5.

Vlad1618 [11]

Answer:

2.5

Step-by-step explanation:

5 0

2 years ago

There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class ha

Paraphin [41]

Answer:

1. 45/482 of the students are in grade 4.

2. 5/9 of the students of the grade 4 are boys.

3. 7/15 of the grade 4 students are in Ms. Ashley's class

4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.

5. There are 14 students with glasses and 7 without glasses.

Step-by-step explanation:

1. Let's review the information given to us for solving the questions:

Number of students in the school = 482

Ms. Ashley's Grade 4 class = 21 students

Ms. Ashley's Grade 4 class boys = 15 students

Ms. Ashley's Grade 4 class girls = 6 students

Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students

Mr. Ben's Grade 4 class = 24 students

Mr. Ben's Grade 4 class boys = 10 students

Mr. Ben's Grade 4 class girls = 14 students

Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students

2. Let's answer all the questions:

1. What fraction of the students in the school are in grade 4?

(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school

21 + 24 / 482 = 45/482

2. What fraction of the grade 4 students are boys?

(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

15 + 10 / 21 + 24

25 / 45 = 5/9

3. What fraction of the grade 4 students are in Ms. Ashley's class?

Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

21 / 21 + 24

21 / 45 = 7/15

4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?

(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class

24 - 6 / 24

18 / 24 = 3/4

5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?

There are 14 students with glasses and 7 without glasses.

4 0

2 years ago