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3 years ago

14

Justify 3x - 6 + 5x = 26

1 answer:

Andru [333]3 years ago

3 0

The answer your looking for is X=4

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Studentka2010 [4]

Fortnite 67Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

4 years ago

Jolene is making a line graph showing that the cost of grain is proportional to the number of pounds purchased. Jolene will plot

Gelneren [198K]

Answer:

a. $(1,0.25)$

b. $y = 0.25x$

Step-by-step explanation:

Given

The data in the table

Solving (a): The coordinate that represents the unit rate

The unit rate is when its 1 pound

This is so because the unit rate is dollars per pounds.

<em>Hence, the coordinate is </em> $(1,0.25)$ <em></em>

Solving (b): Equation of the graph

First, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$(x_1,y_1) = (1,0.25)$

$(x_2,y_2) = (4,1.00)$

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{1.00 - 0.25}{4 - 1}$

$m = \frac{0.75}{3}$

$m = 0.25$

The equation is then calculated as thus:

$y - y_1 = m(x - x_1)$

This gives:

$y - 0.25 = 0.25(x - 1)$

$y - 0.25 = 0.25x - 0.25$

Make y the subject

$y = 0.25x$

<em>Hence, the equation of the graph is: </em> $y = 0.25x$ <em></em>

6 0

3 years ago

What do you mean by mean (average)?collect the age of 8friends and calculate their average ages.

Arada [10]

Answer:

its basically the average

Step-by-step explanation:

To find it,add up all the numbers and then the answer that you get,you divide it by the amount of numbers you added up...

Hopefully this helped

7 0

3 years ago

nekit [7.7K]

Answer:

2

Step-by-step explanation:

6 0

3 years ago