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2 years ago

Tatum exercised for 55 minutes. 10% of that

Mathematics

1 answer:

vazorg [7]2 years ago

4 0

Answer:

5.5 minutes

Step-by-step explanation:

55/10=5.5

5.5 of 55 is 20%

Or 5 minutes and 30 seconds

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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

Lori had 91 apples and Jay had 68 apples how many apples do they have in all? I don't know if I should multiply 68×91

LenaWriter [7]

Answer:

157

Step-by-step explanation:

You don't need to do any multiplication here. It is a fundamental addition problem.

It is given that Lori has got 91 apples and Jay has got 68 of them. We have to find how many apples do they have together.

The correct solution is to add the numbers together:

91+68=157 apples

7 0

3 years ago

Convert 0.86 into a fraction

balandron [24]

0.86= 86/100 this is because the 6 is in the hundredths place so the denominator is going to be 100

5 0

3 years ago

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Miguel glues a ribbon border around the edges of a 5-inch by 8-inch picture to create a frame. What is the total length of ribbo

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

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2 years ago

Use the substitution of x=e^{t} to transform the given Cauchy-Euler differential equation to a differential equation with consta

kherson [118]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dt}=x\dfrac{\mathrm dy}{\mathrm dx}$

which follows from $x=e^t\implies t=\ln x\implies\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x$ .

$\dfrac{\mathrm dy}{\mathrm dt}$ is then a function of $x$ ; denote this function by $f(x)$ . Then by the product rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}$