1+1= I need help please I am just seeing if this app really work

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

2 years ago

PLEASE ANSWERRRRRRR! THANKS!!!!!!!!!!!!!!!!!!!!!! Solve for x. 57 = 3x + 12

Blizzard [7]

57-12= 3x+12-12

45=3x

Divide by 3

x=15

Check answer

57= 3(15)+12

57=57

Answer is correct.

x= 15

6 0

3 years ago

Please help solve with working much appreciated!

Lapatulllka [165]

The right answer is Option A.

Step-by-step explanation:

Given,

Heart rate goal = I

Heart rate reserve = H

70% of H = $\frac{70}{100}H = 0.7H$

Resting heart rate = R

According to given statement,

70% of heart rate reserved is added to resting heart rate to calculate heart rate goal, therefore,

I = R + 0.7H

I=R+0.7H represents the given situation.

The right answer is Option A.

Keywords: linear expression, addition

Learn more about addition at:

#LearnwithBrainly

8 0

3 years ago

Seventh graders collected some gold sand on a class field trip.

satela [25.4K]

Answer:

Class 7A collected 4.8 ounces of pure gold.

Step-by-step explanation:

Key skills required are: Percentages, Multiplication

We only need the information about Class 7A. They collected 40 oz that contains 12% gold.
In other words, this means that 12% of that 40 oz gold sand is pure gold.

Here we have to do 12% x 40 to find the number of oz of pure gold. We first have to convert 12% into a decimal. Divide it by a 100 (or move the decimal point 2 places to the left) and you will get 0.12.

Do 0.12 x 40 and you will get 4.8

Therefore, there are 4.8 oz of pure gold in Class 7A's gold sand

3 0

2 years ago

Given that AB:BC is 4:3 and AC = 56. Find AB. A B

Phantasy [73]

Answer:

ab=32

Step-by-step explanation:

ab:bc

4:3

abc= 56

4+3=7

56÷7=8

ab= 8x4=32

bc=8x3=24 #

3 0

2 years ago