Find the prod (4x+5)(5x +9) OA. 0.2

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

3 years ago

Solve the quadratic equation: 2(x-3)^2-24-0

Keith_Richards [23]

Answer:

x=3+2×sqrt(3)

x=3-2×sqrt(3)

Step-by-step explanation:

2(x-3)²-24=0

2(x-3)²=24

(x-3)²=12

Case 1:

x-3=sqrt(12)=2×sqrt(3)

x=3+2×sqrt(3)

Case 2:

x-3=-sqrt(12)=-2×sqrt(3)

x=3-2×sqrt(3)

7 0

2 years ago

Solve the equation below using a graphing

UNO [17]

Answer:

x = 0.05

x = 1.57

Step-by-step explanation:

The given equation is:

$e^x-\ln 2x = 3.7$

Moving all terms to the left side:

$e^x-\ln 2x - 3.7=0$

Now we define a function:

$y=f(x)=e^x-\ln 2x - 3.7$

The solutions of the equation are the values of x such that y=0.

Since the function cannot be solved by algebraic methods, we use a graphing tool.

Those points where the graph crosses the x-axis are solutions of the equation.

Please refer to the graph in the figure below.

We can clearly identify there are two solutions at

x = 0.05

x = 1.57

6 0

2 years ago

Given two different circles O and Q, which of the following cases presents two circles with no (zero) common tangents?

borishaifa [10]

Concentric circles because if a line is tangent to one circle, it would only intersect teh other

3 0

3 years ago

Read 2 more answers

What integer increased by - 12 is 28?

guajiro [1.7K]

Answer:

40

Step-by-step explanation:

Let n represent the integer. Then the increase can be written as ...

n + (-12) = 28

We can add 12 to both sides of this equation:

n + (-12) + (+12) = 28 +12

n + 0 = 40 . . . . . . -12 and 12 total to zero; 28 and 12 total to 40.

n = 40

The integer is 40.

4 0

2 years ago