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3 years ago

Change 2.6 from decimal to fractions show explanation

Mathematics

1 answer:

noname [10]3 years ago

8 0

Answer:

Step-by-step explanation:

The 2 in 2.6 is in the ones place so we know that it equals 200. The 6 in 2.6 is in the tenths place so we know that it equals 60. Add 200 with 60 to get 260/10. The denominator is 10 because 2.6 only extends to the tenths place.

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A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

scoray [572]

Answer:

a) $P(t) = 660 e^{\frac{ln(6)}{6} t}$

b) $P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

Step-by-step explanation:

For this case we have the following info:

$P(0) = 660$ represent the initial amount of bacteria

$P(6) = 3960$ represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

$\frac{dP}{dt}= kP$

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

$\frac{dP}{P} = k dt$

And if we integrate both sides we got:

$ln |P|= kt + C$

Now if we apply exponential we got:

$P = e^{kt +c}= e^{kt} e^C$

$P(t)= P_o e^{kt}$

For this case using the initial condition:

$660 = P_o e^{0k}, P_o = 660$

We have the following model:

$P(t) = 660 e^{kt}$

Using the second condition $P(6) = 3960$ we have this:

$3960 = 660e^{6k}$

We can divide both sides by 660 and we got:

$6= e^{6k}$

Now we can apply natural log on both sides and we got:

$ln (6)= 6k$

$k = \frac{ln(6)}{6}=0.2986265782$

So then the model would be given by:

$P(t) = 660 e^{\frac{ln(6)}{6} t}$

Part b

For this case we just need to replace t=3 into the model and we got:

$P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617$

4 0

3 years ago

The graph of the function is symmetric with respect to the origin. f(x)=(1/5x)-x^19. T or F

ArbitrLikvidat [17]

Answer: True

Step-by-step explanation:

I already took this part of the quiz and this was the right answer

3 0

3 years ago

Make an expression using -4 or +4 four times to get the equal integer..

Ilia_Sergeevich [38]

Answer:

(4/4)*(4/4) = 1.

Step-by-step explanation:

(4/4)*(4/4) = 1.

8 0

3 years ago

What is the answer to this equation? 2x +3=9

Mariulka [41]

Answer:

X=3

Step-by-step explanation:

6 0

4 years ago

Solve the system of equations below.

sergey [27]

Answer:

A. (3, -3)

Step-by-step explanation:

Let's use the addition/elimination for this to avoid fractions. You could solve one of the equations for y or x and then sub that value into the other equation, but you would have to deal with fractions along the way, so let's just not. Using the addition/elimination (they're the same thing; math books sometimes use one or the other), we line up our equations:

5x + 2y = 9

2x - 3y = 15

It looks like if we want to eliminate the y terms, we can multiply the top equation by 3 and the bottom equation by 2 to get a whole new set of equations:

15x + 6y = 27

4x - 6y = 30

Now we can see that when we add down the columns, the y's cancel each other out. 6y's minus 6y's leaves us with no y's. What we are left with is

19x = 57 so

x = 3.

Now we will sub that 3 back in to either of the original equations to solve for y:

2(3) - 3y = 15 and

6 - 3y = 15 and

-3y = 9 so

y = -3

The solution set then is (3, -3)

8 0

4 years ago