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3 years ago

In function y=f(x), the ? Contains as the possible values of X, while the ? Contains all the possible values of y.

Mathematics

2 answers:

vekshin13 years ago

4 0

What are you even asking ?

bonufazy [111]3 years ago

3 0

Answer: domain, range

Step-by-step explanation:

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what is the equation (in slope-intercept form) of a line that passes through the point (3,-2) and has a slope of -2

Tpy6a [65]

Answer:

$y = - 2x + 4$

Step-by-step explanation:

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2 years ago

Showing work what does 9-6÷3 equal

sashaice [31]

9-(6/3)=9-2=7
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3 years ago

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Len [333]

Answer:

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Step-by-step explanation:

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3 years ago

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

The area, A, of a square whose side length is n

Basile [38]

Step-by-step explanation:

the area of a square is the length multiplied the breadth

in a square, all sides are equal so:

A=n×n

A=n²

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3 years ago