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3 years ago

PLZ I need help. Will give brianliest.

Mathematics

1 answer:

Leno4ka [110]3 years ago

3 0

Answer:

Search it on google and copy and paste it’s easier rather than wasting your points

Step-by-step explanation:

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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

joseph is shopping for school supplies he can buy a box of 24 pens for $4.32 or a box of 36 pens for $5.76. which is a better bu

Ugo [173]

I would say it’s better to buy the 36 box pens. 24\4.32=5.6 on the other hand the box of 36 is 36/5.76=6.25

8 0

2 years ago

Is 6/11 greater than 9/14

4vir4ik [10]

No because when you cross multiply 9/24 has a bigger number

3 0

3 years ago

The sandwiches at the bakery come in four sizes:

kaheart [24]

13 kids sandwiches X 4 inches = 52 inches
22 small sandwiches X 6 inches = 132 inches
17 medium sandwiches X 8 inches = 136 inches
17 large sandwiches X 12 inches = 204 inches

52+132+136+204= 524 inches = 43.66 feet = 43.7 feet

7 0

3 years ago

Let Upper A equals left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 2 2nd Column 4 2nd Row 1st Column 1 2nd Column 3

Anastaziya [24]

Answer:

See explanation

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}-2&4\\1&3\end{array}\right]$

$B=\left[\begin{array}{cc}-2&1\\3&7\end{array}\right]$

A. Find AB:

$AB=\left[\begin{array}{cc}-2&4\\1&3\end{array}\right]\cdot \left[\begin{array}{cc}-2&1\\3&7\end{array}\right]=\left[\begin{array}{cc}-2\cdot (-2)+4\cdot 3&-2\cdot 1+4\cdot 7\\1\cdot (-2)+3\cdot 3&1\cdot 1+3\cdot 7\end{array}\right]=\left[\begin{array}{cc}16&26\\7&22\end{array}\right]$

B. Find BA:

$BA=\left[\begin{array}{cc}-2&1\\3&7\end{array}\right]\cdot \left[\begin{array}{cc}-2&4\\1&3\end{array}\right]=\left[\begin{array}{cc}-2\cdot (-2)+1\cdot 1&-2\cdot 4+1\cdot 3\\3\cdot (-2)+7\cdot 1&3\cdot 4+7\cdot 3\end{array}\right]=\left[\begin{array}{cc}5&-5\\1&33\end{array}\right]$

C. Answers are not the same

D. Matrices multiplication is not commutastive in general, so

$AB\neq BA$

7 0

3 years ago