A shopper buys 3 notebook for $5 each the percent of sales tax is 8% how much is the total sale

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

02

Marrrta [24]

Answer:

Susan is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.

23

20

8 0

2 years ago

Write a system of linear inequalities represented by the graph.

Helga [31]

2,3 or 4,1 either one

6 0

2 years ago

The diagonals of a kite are 22 feet and 33 long. what is the area ?

Goshia [24]

Answer:

A=363

Step-by-step explanation:

To solve the area of a kite you use

$a = \frac{pq}{2}$

So 22×33=726 then divide that by 2 and you get 363.

7 0

3 years ago

A cuboid measures 6cm by 3cm by 2cm Draw a net of the cuboid

Tresset [83]

Answer:

See attachment for cube

Step-by-step explanation:

Given

$Length = 6cm$

$Width = 3cm$

$Height = 2cm$

Required

The net of the cuboid

A cuboid has 6 faces.

The dimension of these faces are:

Length and Width; Length and Height;

Width and Height; Width and Height;

This means that the faces will have the following dimensions:

6cm by 3cm; 6cm by 2cm

3cm by 2cm; 3cm by 2 cm

Taking into account the above measurements and dimensions, you draw 6 faces, then join similar sides lengths.

See attachment for net of the cuboid

4 0

2 years ago