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3 years ago

Today, Alonso walked 1 mile in 0.5 hours.

Mathematics

1 answer:

klemol [59]3 years ago

6 0

Answer:

The answer is Y=3x

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:

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

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3 years ago

A bag contains 4 yellow marbles, 8 blue marbles, and 10 red marbles. If a marble is drawn from the bag, replaced, and another ma

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well if you take the possibility and split it in half the you get your probability of it being

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2 years ago

On a coordinate plane, lockers is 5 units to the left and 3.5 units up. Water fountain is 2.5 units to the left and 3 units up.

VLD [36.1K]

Answer:

it's d water fountain

Step-by-step explanation:

hope this helps edge 2021 Jan 08

7 0

2 years ago

Read 2 more answers

Elimination method - -4x = 4y 4x - 8y = 12

nika2105 [10]

Answer: (4,-4)

y=-4, x=4

Step-by-step explanation:

-4x=4y

4x-8y=12

-8y=-4x+12 Now I can substitute -4x for 4y

-8y=4y+12

-2y=y+12

-3y=12

y=-4

-4x=4y

-4x=4(-4)

x=4

6 0

3 years ago

After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y). A student determined y to be –2. Evaluate the

crimeas [40]

That would not be right because 4 times 3 equals 12 and -6 times 3 equals -18.

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3 years ago